Harold S. Shapiro | Academic Influence

Harold S. Shapiro's AcademicInfluence.com Rankings

Harold S. Shapiro

Mathematics

#330

World Rank

#702

Historical Rank

#158

USA Rank

Measure Theory

#670

World Rank

#913

Historical Rank

#270

USA Rank

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Mathematics

Harold S. Shapiro's Degrees

PhD Mathematics University of California, Berkeley
Bachelors Mathematics University of California, Berkeley

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Why Is Harold S. Shapiro Influential?

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According to Wikipedia, Harold Seymour Shapiro was a professor of mathematics at the Royal Institute of Technology in Stockholm, Sweden, best known for inventing the so-called Shapiro polynomials and for work on quadrature domains.

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Harold S. Shapiro's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

The Schwarz Function and Its Generalization to Higher Dimensions (1992) (291)
Cyclic vectors and invariant subspaces for the backward shift operator (1970) (260)
On Some Interpolation Problems for Analytic Functions (1961) (258)
Extremal problems for polynomials and power series (1951) (232)
Topics in Approximation Theory (1971) (227)
Ethical issues in the design and conduct of clinical trials in developing countries. (2001) (213)
Domains on which analytic functions satisfy quadrature identities (1976) (196)
A Combinatory Detection Problem (1963) (161)
A Unified Approach to Certain Problems of Approximation and Minimization (1961) (148)
On the zeros of functions with finite Dirichlet integral and some related function spaces (1962) (144)
Poincaré’s Variational Problem in Potential Theory (2007) (123)
Some theorems on Čebyšev approximation (1963) (115)
Criteria for Evaluation of Econometric Models (1972) (112)
An algebraic theorem of E. Fischer, and the holomorphic Goursat problem (1989) (108)
On certain extremum problems for analytic functions (1953) (107)
Singular measures and domains not of Smirnov type (1966) (103)
Contractive zero-divisors in Bergman spaces (1993) (103)
What is a Quadrature Domain (2005) (102)
Smoothing and Approximation of Functions (1970) (82)
On the Mathematical Theory of Error-Correcting Codes (1959) (79)
The Dynamics of Household Budget Allocation to Food Expenditures (1976) (70)
A Larger Sense of Purpose: Higher Education and Society (2005) (63)
Dirichlet's Problem When the Data is an Entire Function (1992) (62)
Comparison theorems for a generalized modulus of continuity (1969) (61)
Invariant subspaces in Bergman spaces and the biharmonic equation. (1994) (60)
Employment and Health Benefits: A Connection at Risk (1995) (60)
The allocation of household income to food consumption (1976) (59)
Certain Hilbert spaces of entire functions (1966) (55)
Weakly invertible elements in certain function spaces, and generators in ${\cal l}_1$. (1964) (52)
The Models of Project LINK. (1978) (52)
A tauberian theorem related to approximation theory (1968) (49)
Alias-Free Sampling of Random Noise (2018) (48)
An Elementary Proof That the Biharmonic Green Function of an Eccentric Ellipse Changes Sign (1994) (48)
Ethical and policy issues of human cloning. (1997) (46)
Jackson’s Theorem in Higher Dimensions (1964) (46)
Generalized Analytic Continuation (2002) (41)
Belmont revisited : ethical principles for research with human subjects (2005) (41)
The Taylor coefficients of inner functions. (1962) (40)
Some negative theorems of approximation theory. (1964) (38)
MAJORANT PROBLEMS FOR FOURIER COEFFICIENTS (1975) (38)
The level curves of harmonic functions (1966) (37)
Universities and Their Leadership (1998) (36)
Unbounded quadrature domains (1987) (36)
The Friedrichs operator of a planar domain. II (2000) (32)
Some Remarks on Weighted Polynomial Approximations of Holomorphic Functions (1967) (32)
Extremal functions in invariant subspaces of Bergman spaces (1996) (30)
Two-dimensional shapes and lemniscates (2010) (30)
An Arithmetic Function Arising From the /phi Function (1943) (29)
Remarks on the reflection principle for harmonic functions (1990) (28)
A minimal area problem in conformal mapping (1999) (28)
Macro-Econometric Model Building in Socialist and Non-Socialist Countries: A Comparative Study (1976) (27)
On cyclic vectors of the backward shift (1967) (26)
Some Tauberian theorems with applications to approximation theory (1968) (26)
On Domains in Which Harmonic Functions Satisfy Generalized Mean Value Properties (1997) (26)
Oligopoly Theory and Retail Food Pricing (1964) (26)
National Bioethics Advisory Commission (2001) (26)
On Zero and One Points of Analytic Functions (1995) (25)
Some uniqueness problems in approximation theory (1960) (24)
On the classical Dirichlet problem in the plane with rational data (2006) (23)
Functions with a spectral gap (1973) (21)
Macroeconometric Models of the Soviet Union and Eastern European Economies: A Tabular Survey (1977) (21)
The expansion of mean-periodic functions in series of exponentials (1958) (21)
An Inverse Problem for the Double Layer Potential (2001) (21)
Ethical Dilemmas and Stem Cell Research (1999) (20)
Approximation by Generalized Rational Functions (1964) (20)
Restriction operators, balayage and doubly orthogonal systems of analytic functions (2003) (20)
The Choice of Optimal Intermediate Economic Targets (1970) (19)
Algebraic Aspects of the Dirichlet Problem (2005) (19)
Lebesgue constants for spherical partial sums (1975) (19)
The willingness to risk failure. (1990) (18)
Functional equations and harmonic extensions (1994) (18)
Extremal Problems for Nonvanishing Functions in Bergman Spaces (2005) (18)
The cauchy-kowalevskaya theorem and generalizations (1995) (18)
The mixed Cauchy problem for holomorphic partial differential operators (1995) (17)
A FREE BOUNDARY PROBLEM RELATED TO SINGLE-LAYER POTENTIALS (2002) (17)
Problems for Solution: 4603-4607 (1954) (16)
The Demand for Money: A Note from the Time Series (1964) (16)
Monotonic singular functions of high smoothness. (1968) (16)
Best approximation in the mean by analytic and harmonic functions (1999) (16)
Consumer Attitudes, Buying Intentions and Expenditures: An Analysis of the Canadian Data (1969) (16)
COMPENSATING‐BALANCE REQUIREMENTS: THE RESULTS OF A SURVEY (1964) (16)
Is Verification Possible? The Evaluation of Large Econometric Models (1973) (15)
Some theorems on Čebyšev approximation II (1967) (15)
Weakly Invertible Elements in the Space of Square-Summable Holomorphic Functions (1974) (15)
Reflections on the Interface of Bioethics, Public Policy, and Science (1999) (14)
Remarks concerning domains of Smirnov type. (1966) (14)
A minimal area problem in conformal mapping II (2001) (14)
The vekua hull of a plane domain (1990) (14)
Regularity properties of the element of closest approximation (1973) (13)
Domains Allowing Exact Quadrature Identities for Harmonic Functions — An Approach Based on P.D.E. (1984) (13)
Unimodular functions and uniform boundedness (1989) (12)
Extending Solutions of Holomorphic Partial Differential Equations Across Real Hypersurfaces (1998) (11)
Reconstructing a function from its values on a subset of its domain—a Hilbert space approach (1986) (11)
Interpolation in $H^{p}$ spaces (1972) (10)
Overconvergence of sequences of rational functions with sparse poles (1968) (10)
Econometric Review of Alternative Fiscal and Monetary Policies, 1971-75 (1978) (10)
A Dialogue on Competitiveness. (1988) (10)
Remarks concerning cyclic vectors in Hardy and Bergman spaces. (1991) (9)
Energy spreading and data compression using the Prometheus Orthonormal Set (1996) (9)
Some Initial Reflections on NBAC (2002) (9)
Employment and Health Benefits (1993) (9)
Fischer spaces of entire functions (1968) (8)
Analytic continuation of Jacobi polynomial expansions (1997) (8)
Revealing the Hidden Nature of Space and Time : Charting the Course for Elementary Particle Physics Committee on Elementary Particle Physics in the 21 st Century , National Research Council (2005) (8)
Compensating-Balance Requirements: The Theory and Its Implications (1964) (8)
Analytic continuation of Dirichlet series (1995) (8)
The Structure and Properties of the Michigan Qtrly Econometric Model of the U.S. Economy (1974) (8)
A uniform boundedness principle concerning inner functions (1988) (8)
Approximation by Trigonometric Polynomials to Periodic Functions of Several Variables (1969) (7)
Invariant subspaces in Bergman spaces and Hedenmalm's boundary value problem (1994) (7)
Algebraicity in the Dirichlet problem in the plane with rational data (2007) (7)
A Weighted L1 Estimate for the Laplace Operator (1990) (7)
The functions and resources of the American University of the twenty-first century (1992) (7)
Spectral Aspects of a Class of Differential Operators (2002) (6)
A Model of Macroeconomic Activity, Volume I: A Theoretical Model.@@@A Model of Macroeconomic Activity, Volume II: The Empirical Model. (1977) (6)
Interpolation in Hilbert spaces of analytic functions (1963) (6)
Alternative proofs of a theorem of Moyls and Marcus on the numerical range of a square matrix (1980) (6)
Almost persuaded: reactions to Oldham et al. (1999) (6)
On the linear independence of Laplace integral solutions of certain differential equations (1961) (6)
Best approximation in the supremum norm by analytic and harmonic functions (2001) (6)
A planar face on the unit sphere of the multiplier space _{}, 1<<∞ (1972) (6)
Toeplitz operators in Segal-Bargmann spaces of vector-valued functions vector-valued functions (2003) (6)
A Class of Singular Functions (1968) (5)
Virial Series of the Ideal Bose-Einstein Gas (1955) (5)
A Quasi Maximum Principle for Holomorphic Solutions of Partial Differential Equations in Cn (1997) (5)
A Planar Face on the Unit Sphere of the Multiplier Space M p , 1 < p < ∞ (1972) (5)
On generators of the Banach algebras ₁ and ₁(0,∞) (1963) (5)
The Efficacy of Monetary and Fiscal Policy: A Comment (1971) (5)
GRAPHS AND FUNCTIONAL EQUATIONS (2008) (5)
Fourier Multipliers whose Multiplier Norm is an Attained Value (1972) (5)
On Generators of the Banach Algebras l 1 and L 1 (0 (1963) (5)
Minimal area problems for functions with integral representation (2006) (5)
Current Realities and Future Prospects. (1993) (5)
Large and small subspaces of Hilbert space. (1965) (5)
Boundary values of bounded holomorphic functions of several variables (1971) (5)
Bounded functions with one-sided spectral gaps. (1972) (4)
Smoothness of the boundary function of a holomorphic function of bounded type (1968) (4)
Regulation of Employment-Based Health Benefits: The Intersection of State and Federal Law (1993) (4)
Commentary on "The use of econometric methods in the analysis of centrally planned economies: The SRI-WEFA experience" by Donald W. Green (1977) (4)
Advanced Problems: 5300-5309 (1965) (4)
On a Uniqueness Property of Harmonic Functions (2008) (4)
Alan Gregg memorial lecture. Medical education and the university. (1986) (4)
A National Research Strategy. (1986) (4)
Paradox, change and choice: an economist's view of some current health care resource issues. (1985) (4)
Incomplete orthogonal families and a related question on orthogonal matrices. (1964) (4)
Pons, Reed-Muller Codes, and Group Algebras (2004) (4)
Problems for Solution: E1396-E1400 (1960) (3)
Perspectives on the Accuracy of Macro-Econometric Forecasting Models (1978) (3)
Higher Education: Some Problems and Challenges in a Changing World. Discussion Series Issue 4. (1994) (3)
The modulus of continuity of an analytic function (1976) (3)
A characterization of certain weak∗-closed subalgebras of L∞ (1977) (3)
Comparative approximation in two topologies (1979) (3)
Some remarks on modular arithmetic and parallel computation (1962) (3)
A characterization of certain weak∗-closed subalgebras of L∞ (1977) (3)
A counterexample in harmonic analysis (1979) (3)
A remark concerning Littlewood’s Tauberian theorem (1965) (3)
Stopping science: human cloning--should it be stopped? (1999) (3)
Ethical considerations and public policy (1999) (3)
Approximation in L1 -Norm by Elements of a Uniform Algebra (1998) (3)
The Very Old , the Nearly New and the Really New : " To Bt or not to Bt " (2001) (3)
Weak compactness in certain star-shift invariant subspaces (2003) (3)
Bioethics and Public Policy’ (2002) (2)
Sister President: Ruth J. Simmons (1995) (2)
Reproducing Kernels and Beurling's Theorem (2015) (2)
COMMITTEE ON EMPLOYER-BASED HEALTH BENEFITS (1993) (2)
A regional econometric forecasting system: Major economic areas of Michigan (1986) (2)
Basic flaws in US human research protection must be addressed (2002) (2)
Teichmller-type annihilators of $L\sp 1$-analytic functions (1990) (2)
Prolongations and Cyclic Vectors (2004) (2)
The Range of an Integer-Valued Polynomial (1957) (2)
Convergence almost everywhere of convolution integrals with a dilation parameter (1976) (2)
A Remark Concerning Littlewoods Tauberian Theorem (1965) (2)
FREE INTERPOLATION OF GERMS OF ANALYTIC FUNCTIONS IN HARDY SPACES (1987) (2)
Reflections on the Future of University-Based Research. (1990) (2)
Origins and Evolution of Employment-Based Health Benefits (1993) (2)
Problems for Solution: 4468-4472 (1952) (2)
Numbers and functions computable by means of rational recurrence formulae (1959) (2)
Regular Functions Satisfying Irregular Ordinary Differential Equations (2003) (2)
Tradition and change: Perspectives on education and public policy (1987) (1)
Problems for Solution: 4528,4543-4547 (1953) (1)
Malmheden's theorem revisited (2009) (1)
Is taking sides a good idea for universities? (1984) (1)
Liberal Education, Liberal Democracy, and the Soul of the University (2009) (1)
Conversations in cloning (1999) (1)
Society in the History of Educational Change: A Brief Review of Studies by Bernard Bailyn and Lawrence Cremin (1978) (1)
Circular a-21 negotiations. (1982) (1)
: A Larger Sense of (2005) (1)
Elementary Problems: E1030,E1075,E2504-E2509 (1974) (1)
Problems for Solution: 4959-4964 (1961) (1)
Ideals Drowned in the Marketplace (2005) (1)
Local solvability of PDE with constant coefficients (1993) (1)
Clear thinking will never be out of date (1985) (1)
What is an embryo?: a comment. (2004) (1)
Some spectral properties of weighted random processes (2015) (1)
Operator Theory and Harmonic Analysis (2001) (1)
Allen lowell shields—some reminiscences (1990) (1)
How Incompatible Worldviews Can Coexist (2014) (1)
Boundary values of bounded holomorphic functions (1972) (1)
Federal Policy Making for Biotechnology, Executive Branch, National Bioethics Advisory Commission (2002) (1)
Scientific progress and ethical issues. (2002) (1)
Advanced Problems: 6090-6095 (1976) (1)
Some orthogonal matrices and related orthogonal functions systems (1966) (1)
Problems for Solutions: E1046-E1050 (1953) (0)
Risk Selection, Risk Sharing, and Policy (1993) (0)
Science , Anxiety and Meaning : Giving Moral Shape to Our National Life (2001) (0)
Participants in Meetings Held in Conjunction with Project (1993) (0)
FOREWORD (2021) (0)
NATIONAL BIOETHICS ADVISORY COMMISSION U.S. Chamber of Commerce Anheuser-Busch Briefing Center 1615 H Street, NW Washington, DC 20062 (2000) (0)
Leading Indicators to Predict Cyclical Turning Points (2007) (0)
Problems for Solution: 4503-4507 (1952) (0)
Some Ethical Dimensions of Scientific Progress (2009) (0)
DETERMINANTS OF HOUSEHOLD FOOD EXPENDITURES 13 7 Income Elasticities and the Marginal Propensity to Consume (2007) (0)
What Does Employer Management of Health Benefits Involve? Overview and Case Study (1993) (0)
5. Thin Rationality Review (1998) (0)
Protection for human subjects in medical research. (2000) (0)
The Transformation of the Antebellum College From Right Thinking to Liberal Learning (2009) (0)
Changing in a World of Change (1995) (0)
Book reviews (1984) (0)
Conclusion. Law on the Margin (1998) (0)
Risk, progress, and achievement (1991) (0)
2. Separation of Powers without Idolatry (1998) (0)
4. Rationally Arbitrary Decisions (1998) (0)
Index of Cases (1998) (0)
CHAPTER 3. Cognition, Character, and Culture in Undergraduate Education: Rhetoric and Reality (2020) (0)
THE STRUCTURE AND PROPERTIES OF THE MICHIGAN (2016) (0)
Opinion Surveys on Employment-Based Health Benefits and Related Issues (1993) (0)
Revisiting the guiding principles of research ethics (2006) (0)
Advanced Problems: 6246-6251 (1979) (0)
Response : Academic Freedom (1984) (0)
Introduction. The Abnegation of Law’s Empire (1998) (0)
Whatever happened to the colonial colleges (1993) (0)
Problems for Solution: 4474, 4478-4482 (1952) (0)
Government Sector Equations for Macroeconomic Models.@@@The Dynamics of RDXI. (1971) (0)
Academic freedom [5] (1984) (0)
In reply: academic freedom. (1984) (0)
The University and Society (2009) (0)
Employment-Based Health Benefits Today (1993) (0)
3. Deference and Due Process (1998) (0)
"Ethical Issues in Human Stem Cell Research: Executive Summary" (1999), by the US National Bioethics Advisory Commission (2017) (0)
Balance-of-Payments Adjustment Policies: Japan, Germany, and the Netherlands. (1968) (0)
Harold T. Shapiro, PhD. (2000) (0)
The Social and Political Challenge of Inflation: An Economist's View (1981) (0)
Findings and Recommendations (1993) (0)
Nobelist Professor Toni Morrison: An Academic Celebration. (1994) (0)
6. How Law Empowers Nonlawyers (1998) (0)
1966〜75年の選択的財政金融政策の計量経済学的考察-2- (1976) (0)
A Hilltop History : Early landscape architects charmed by ' vantage point , ' liken it to Greece ' s Acropolis (2014) (0)
Glossary and Acronyms (1993) (0)
Princeton and Asia in the Twenty-First Century (1997) (0)
Monetary and Fiscal Influences on U.S. Money Income, 1891-1970: Comment (1973) (0)
Conversations in cloning: The Genetic Revolution and Human Rights: The Oxford Amnesty Lectures 1998, edited by Justine Burley. (1999) (0)
Dolly's big adventure (1997) (0)
Book Review Germ-Line Intervention and Our Responsibilities to Future Generations (Philosophy and Medicine. Vol. 55.) Edited by Emmanuel Agius and Salvino Busuttil, in collaboration with Tae-Chang Kim and Katsuhiko Yazaki. 174 pp. Dordrecht, the Netherlands, Kluwer Academic, 1998. $120. 0-7923-4828- (1999) (0)
mentary on “ ‘ The Use of EC e Analysis of Centrally SRI-WEFA Experienc (2003) (0)
Foreword, Preface, List of Abbreviations (1996) (0)
1. The Legality of Administrative Law (1998) (0)
Letter from Harold T. Shapiro, National Bioethics Advisory Commission to Harold Varmus (1999) (0)
Health Care Costs: More Questions than Answers (1993) (0)
Problems for Solution: E926-E930 (1950) (0)
Erratum to “the cauchy-kowalevskaya theorem and generalizations” (1995) (0)
Advanced Problems: 5490-5499 (1967) (0)
Best uniform approximation (1971) (0)
Problems for Solution: 4623-4627 (1955) (0)
Elementary Problems: E1985-E1994 (1967) (0)
Continuation by formal multiplication of series (2002) (0)
The impact of the geographic dispersal of displaced households in urban renewal programs : Vancouver, a case study (1969) (0)
Constrained Approximation via Functional Analysis (2011) (0)
The Poincaré example (2002) (0)
The generalized modulus of continuity and wavelets (1994) (0)
The Limitations of the Cauchy-Kovalevsky Theorem (2002) (0)
Problems for Solution: 4573-4577 (1954) (0)
Approximation theory in homogeneous Banach spaces (1971) (0)
Minimal extrapolation of Fourier transforms (1971) (0)
Advanced Problems: 5143,5191-5199 (1964) (0)
Bilinear representation formulas for polynominals. (1988) (0)
Problems for Solutions: E1071-E1075 (1953) (0)
Problems for Solution: E1501-E1505 (1962) (0)
ON GENERATORS OF THE BANACH ALGEBRAS (2010) (0)
The interpolation formula and Gaussian quadrature (1971) (0)
The Winding of an Analytic Function. (1974) (0)
ON GENERATORS OF THE BANACH ALGEBRA L SUB 1 (0, INFINITIVE) AND RELATED QUESTIONS (1960) (0)
Advanced Problems: 5200-5208 (1964) (0)
Applications of the Hahn-Banach theorem and dual extremal problems (1971) (0)
Smoothing and Approximation of Functions[MatSciRep:55] (1967) (0)
Some Theorems on deby3ev Approximation II (1967) (0)
Problems for Solution: 4965-4970 (1961) (0)
Approximation Theory and “Domain of Dependence” for P.D.E. of Hyperbolic Type (1982) (0)
Isolated Singularities of Harmonic Functions (2003) (0)
General aspects of "Degree of approximation" (1971) (0)
Approximation theory and extremal problems in Hilbert spaces (1971) (0)
Problems for Solution: 4653-4657 (1955) (0)
Advanced Problems: 5253-5260 (1965) (0)
Best approximation and extremal problems in other norms (1971) (0)
Problems for Solution: 5058-5064 (1962) (0)
Problems for Solution: E1051-E1055 (1953) (0)
Problems for Solution: 4893-4898 (1960) (0)
Problems for Solution: 4663-4667 (1955) (0)
Problems for Solution: 5051-5057 (1962) (0)
Problems for Solution: 4877, 4887-4892 (1960) (0)
UNIFORM ALGEBRAS ON CURVES (2007) (0)
On generators of the Banach algebras $l\sb{1}$ and $L\sb{1}(0,\,\infty )$ (1963) (0)
Borel’s ideas and their later development (2002) (0)
Problems for Solution: 4933, 4953-4958 (1961) (0)
Notation and preliminaries (2002) (0)
A continuation involving almost periodic functions (2002) (0)

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