Joseph L. Walsh
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Most Influential Person Across History
American mathematician
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Why Is Joseph L. Walsh Influential?
(Suggest an Edit or Addition)According to Wikipedia, Joseph Leonard Walsh was an American mathematician who worked mainly in the field of analysis. The Walsh function and the Walsh–Hadamard code are named after him. The Grace–Walsh–Szegő coincidence theorem is important in the study of the location of the zeros of multivariate polynomials.
Joseph L. Walsh'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 theory of splines and their applications (1969) (1936)
- Interpolation and Approximation by Rational Functions in the Complex Domain (1935) (1284)
- A Closed Set of Normal Orthogonal Functions (897)
- The approximation of harmonic functions by harmonic polynomials and by harmonic rational functions (1929) (108)
- The Location of Critical Points of Analytic and Harmonic Functions (1950) (103)
- On the location of the roots of certain types of polynomials (1922) (90)
- On approximation by euclidean and non-euclidean translations of an analytic function (1941) (64)
- On the Derivatives of Functions Analytic in the Unit Circle. (1938) (51)
- Overconvergence, degree of convergence, and zeros of sequences of analytic functions (1946) (48)
- On approximation to an analytic function by rational functions of best approximation (1934) (45)
- History of the Riemann Mapping Theorem (1973) (44)
- A mean value theorem for polynomials and harmonic polynomials (1936) (42)
- The existence of rational functions of best approximation (1931) (40)
- Integrated continuity conditions and degree of approximation by polynomials or by bounded analytic functions (1959) (39)
- FUNDAMENTAL PROPERTIES OF GENERALIZED SPLINES. (1964) (35)
- On the conformal mapping of multiply connected regions (1956) (35)
- Interpolation and approximation (1935) (32)
- Complex cubic splines (1967) (29)
- Equilibrium of inverse-distance forces in three-dimensions (1973) (27)
- On the location of the roots of the Jacobian of two binary forms, and of the derivative of a rational function (1918) (27)
- The analogue for maximally convergent polynomials of Jentzsch’s theorem (1959) (27)
- Polynomials of best approximation on a real finite point set. I (1959) (24)
- On the asymptotic behavior of polynomials with extremal properties, and of their zeros (1954) (24)
- An Inequality for the Roots of An Algebraic Equation (1924) (24)
- On the degree of polynomial approximation to harmonic and analytic functions (1949) (23)
- Sufficient conditions for various degrees of approximation by polynomials (1940) (22)
- CONVERGENCE PROPERTIES OF GENERALIZED SPLINES. (1965) (21)
- Least pth Power Polynomials on a Real Finite Point Set (1955) (21)
- A generalization of Faber's polynomials (1958) (21)
- Note on the location of zeros of the derivative of a rational function whose zeros and poles are symmetric in a circle (1939) (21)
- Interpolation And Approximation By The Rational Functions (19)
- On the Degree of Convergence of Solutions of Difference Equations to the Solution of the Dirichlet Problem (1954) (19)
- A Bibliography on orthogonal polynomials : Report of the commitee on A Bibliography on orthogonal polynomials Division of Ohysical Sciences National Research Council (1940) (19)
- On the Location of the Roots of the Derivative of a Polynomial. (1920) (19)
- Padé approximants as limits of rational functions of best approximation, real domain (1974) (19)
- On the accuracy of the numerical solution of the Dirichlet problem by finite differences (1953) (17)
- The convergence of sequences of rational functions of best approximation (1964) (17)
- Properties of analytic splines (I) complex polynomial splines (1969) (17)
- Approximation by polynomials in the complex domain (1935) (16)
- Complex polynomial splines on the unit circle (1971) (16)
- On Pellet's Theorem Concerning the Roots of a Polynomial (1924) (16)
- On interpolation and approximation by rational functions with preassigned poles (1932) (16)
- POLYNOMIALS OF BEST APPROXIMATION ON AN INTERVAL, II. (1959) (15)
- Extremal, orthogonality, and convergence properties of multidimensional splines (1965) (15)
- Least th power polynomials on a finite point set (1956) (15)
- Interpolation and functions analytic interior to the unit circle (1932) (15)
- Lemniscates and Equipotential Curves of Green's Function (1935) (14)
- LEAST P-TH POWER POLYNOMIALS ON A REAL FINITE POINT SET (1955) (14)
- Note on Degree of Approximation to an Integral by Riemann Sums (1937) (14)
- Least squares and interpolation in roots of unity (1964) (14)
- Possibility of Uniform Rational Approximation in the Spherical Metric (1976) (14)
- On the Convergence of the Sturm-Liouville Series (1922) (13)
- On the derivative of a polynomial and Chebyshev approximation (1953) (13)
- On approximation by bounded analytic functions (1954) (13)
- Degree of Approximation on a Jordan Curve. (1952) (13)
- On canonical conformal maps of multiply connected domains (1959) (13)
- Polynomial approximation to harmonic and analytic functions: generalized continuity conditions (1950) (12)
- On the convergence of rational functions which interpolate in the roots of unity. (1973) (12)
- POLYNOMIALS OF BEST APPROXIMATION ON AN INTERVAL. (1959) (12)
- On the convergence and overconvergence of sequences of polynomials of best simultaneous approximation to several functions analytic in distinct regions (1934) (12)
- Underpolynomials and infrapolynomials (1957) (11)
- Extension and some applications of the coincidence theorems (1969) (11)
- Interpolation and orthonormal systems (1952) (11)
- ON GENERALIZED TCHEBYCHEFF POLYNOMIALS. (1956) (10)
- Hyperbolic capacity and interpolating rational functions II (1965) (10)
- BEST APPROXIMATORS WITHIN A LINEAR FAMILY ON AN INTERVAL. (1960) (10)
- Solution of the Dirichlet Problem for the Ellipse by Interpolating Harmonic Polynomials (1960) (9)
- The Cauchy-Goursat Theorem for Rectifiable Jordan Curves. (1933) (9)
- A property of Haar's system of orthogonal functions (1923) (9)
- On the expansion of analytic functions in series of polynomials (1924) (8)
- The zeros of infrapolynomials with some prescribed coefficients (1961) (8)
- Asymptotic behavior of restricted extremal polynomials and of their zeros. (1957) (8)
- Note on Approximation by Bounded Analytic Functions. (1951) (8)
- A theorem of Grace on the zeros of polynomials, revisited (1964) (8)
- A Bibliography of Orthogonal Polynomials (1941) (8)
- Note on the relation between continuity and degree of polynomial approximation in the complex domain (1937) (7)
- Cubic splines on the real line (1968) (7)
- ZEROS OF THE ERROR FUNCTION FOR TCHEBYCHEFF APPROXIMATION IN A SMALL REGION (1963) (7)
- On the degree of polynomial approximation to analytic functions: problem (1941) (7)
- On the Convergence of Sequences of Rational Functions (1967) (7)
- A sequence of rational functions with application to approximation by bounded analytic functions (1963) (7)
- Maximal Convergence of Sequences of Harmonic Polynomials (1937) (6)
- NOTE ON DEGREE OF APPROXIMATION TO ANALYTIC FUNCTIONS BY RATIONAL FUNCTIONS WITH PREASSIGNED POLES. (1956) (6)
- On restricted infrapolynomials (1956) (6)
- Approximation by polynomials: uniform convergence as implied by mean convergence. (1966) (6)
- On Interpolation to Harmonic Functions by Harmonic Polynomials. (1932) (6)
- On Interpolation and Approximation by Functions Analytic and Bounded in a Given Region. (1938) (6)
- Extensions of D. Jackson’s theorem on best complex polynomial mean approximations (1969) (5)
- A Certain Two-Dimensional Locus (1922) (5)
- Note on the degree of convergence of sequences of analytic functions (1940) (5)
- AN INTERPOLATION PROBLEM FOR HARMONIC FUNCrIONS. (1954) (5)
- Approximation by rational functions: Open problems (1970) (5)
- Note on Polynomial Interpolation to Analytic Functions. (1933) (5)
- On the overconvergence of certain sequences of rational functions of best approximation (1931) (5)
- ON REPRESENTATIONS AND EXTENSIONS OF BOUNDED LINEAR FUNCTIONALS DEFINED ON CLASSES OF ANALYTIC FUNCTIONS (1954) (5)
- NOTE ON THE DISTRIBUTION OF ZEROS OF EXTREMAL POLYNOMIALS. (1954) (5)
- On functions analytic in a region: approximation in the sense of least th powers (1949) (5)
- On the expansion of analytic functions in series of polynomials and in series of other analytic functions (1928) (5)
- On the Transformation of Convex Point Sets (1921) (5)
- Taylor's series and approximation to analytic functions (1946) (5)
- On the Shape of Level Curves of Green's Function (1937) (5)
- The zeros of infrapolynomials with prescribed values at given points (1963) (4)
- ON THE OVERCONVERGENCE OF SEQUENCES OF POLYNOMIALS OF BEST APPROXIMATION. (1930) (4)
- The critical points of linear combinations of harmonic functions (1948) (4)
- An extension of the generalized Bernstein lemma (1967) (4)
- On the degree of approximation to an analytic function by means of rational functions (1928) (4)
- NOTE ON THE CONVERGENCE OF APPROXIMATING RATIONAL FUNCTIONS OF PRESCRIBED TYPE. (1963) (4)
- Approximation to a Function by a Polynomial in Another Function (1969) (4)
- Lipschitz Conditions for Harmonic and Discrete Harmonic Functions (1957) (4)
- A New Generalization of Jensen's Theorem on the Zeros of the Derivative of a Polynomial (1955) (4)
- ON THE LOCATION OF THE ZEROS OF SOME INFRAPOLYNOMIALS WITH PRESCRIBED COEFFICIENTS (1964) (4)
- Mean approximation by polynomials on a Jordan curve (1971) (3)
- On the Overconvergence of Sequences of Rational Functions (1932) (3)
- On the degree of approximation to a harmonic function (1927) (3)
- On the location of the zeros of a polynomial whose center of gravity is given (1964) (3)
- On interpolation by functions analytic and bounded in a given region (1939) (3)
- ON THE CONVEXITY OF THE OVALS OF LEMNISCATES (1961) (3)
- Note on degree of trigonometric and polynomial approximation to an analytic function (1938) (3)
- DEGREE OF POLYNOMIAL APPROXIMATION TO AN ANALYTIC FUNCTION AS MEASURED BY A SURFACE INTEGRAL. (1962) (3)
- Note on least-square approximation to an analytic function by polynomials, as measured by a surface integral (1959) (3)
- Degree of approximation by rational functions and polynomials. (1968) (3)
- On approximation by rational functions to an arbitrary function of a complex variable (1929) (3)
- The Equivalence of Expansions in Terms of Orthogonal Functions (1922) (3)
- Note on the location on the critical points of Green's function (1933) (3)
- A generalization of the Fourier cosine series (1921) (3)
- Degree of approximation to functions on a Jordan curve (1952) (3)
- Some examples in degree of approximation by rational functions (1971) (3)
- SURPLUS FREE POLES OF APPROXIMATING RATIONAL FUNCTIONS. (1964) (3)
- On the location of the roots of polynomials (3)
- On Distortion at the Boundary of a Conformal Map. (1950) (3)
- Location of zeros of infrapolynomials (1960) (2)
- On the Critical Points of Functions Possessing Central Symmetry on the Sphere (1948) (2)
- Mean approximation on an interval for an exponent less than one (1966) (2)
- Inequalities expressing degree of convergence of rational functions (1969) (2)
- Note on degree of trigonometric and polynomial approximation to an analytic function, in the sense of least $p$th powers (1940) (2)
- A Duality in Interpolation to Analytic Functions by Rational Functions. (1933) (2)
- On polynomial interpolation to analytic functions with singularities (1932) (2)
- On the degree of convergence of extremal polynomials and other extremal functions (1965) (2)
- Note on the simultaneous orthogonality of harmonic polynomials on several curves (1937) (2)
- An interpolation series expansion for a meromorphic function (1953) (2)
- On continuity properties of derivatives of sequences of functions (1953) (2)
- BOUNDARY VALUES OF AN ANALYTIC FUNCTION AND THE TCHEBYCHEFF METHOD OF APPROXIMATION. (1929) (2)
- On the Solution of Linear Equations in Infinitely Many Variables by Successive Approximations (1920) (2)
- Note on the Shape of Level Curves of Green's Function (1953) (2)
- Approximation by polynomials: uniform convergence as implied by mean convergence, iii. (1966) (2)
- Interpolation and approximation by functions analytic and bounded in a given region (1944) (2)
- Geometry of the zeros of the sums of linear fractions (1965) (2)
- On approximation to an arbitrary function of a complex variable by polynomials (1928) (2)
- NOTE ON INVARIANCE OF DEGREE OF POLYNOMIAL AND TRIGONOMETRIC APPROXIMATION UNDER CHANGE OF INDEPENDENT VARIABLE. (1959) (2)
- Note on the Location of the Critical Points of Harmonic Functions. (1934) (2)
- On simultaneous interpolation and approximation by functions analytic in a given region (1950) (2)
- Interpolation and an Analogue of the Laurent Development. (1933) (2)
- Note on the orthogonality of Tchebycheff polynomials on confocal ellipses (1934) (2)
- MATHEMATICS: POLYNOMIALS OF BEST APPROXIMATION ON A REAL FINITE POINT SET. (1957) (2)
- Note on the Curvature of Level Curves of Green's Function. (1937) (2)
- The divergence of sequences of polynomials interpolating in roots of unity (1936) (1)
- On the Convergence of Rational Functions of Best Approximation to a Meromorphic Function (1972) (1)
- A Theorem on Cross-Ratios in the Geometry of Inversion (1921) (1)
- ON INTERPOLATION TO A GIVEN ANALYTIC FUNCTION BY ANALYTIC FUNCTIONS OF MINIMUM NORM (1955) (1)
- NOTE ON POLYNOMIAL APPROXIMATION ON A JORDAN ARC. (1960) (1)
- A Rigorous Treatment of the First Maximum Problem in the Calculus (1947) (1)
- Note on the shape of level curves of Green’s function (1953) (1)
- Critical Points of Harmonic Functions as Positions of Equilibrium in a Field of Force. (1948) (1)
- On the Circles of Curvature of the Images of Circles Under a Conformal Map (1939) (1)
- Note on the coefficients of overconvergent power series (1942) (1)
- Note on the Curvature of Orthogonal Trajectories of Level Curves of Green's Function. (1937) (1)
- Approximation by bounded analytic functions: General configurations. (1959) (1)
- Note on the curvature of orthogonal trajectories of level curves Green’s function. III (1938) (1)
- Note on the location of the roots of a polynomial (1926) (1)
- On degree of approximation on a Jordan curve to a function analytic interior to the curve by functions not necessarily analytic interior to the curve (1946) (1)
- Approximation on a line segment by bounded analytic functions: Problem (1959) (1)
- On the Expansion of Harmonic Functions in Terms of Harmonic Polynomials. (1927) (1)
- Note on the convergence of sequences of rational functions of best approximation to a meromorphic function. (1972) (1)
- Note on classes of functions defined by integrated Lipschitz conditions (1968) (1)
- On the Location of the Critical Points of Harmonic Measure. (1947) (1)
- On the boundary behavior of a conformal map (1956) (1)
- On the location of the zeros of the derivatives of a polynomial symmetric in the origin (1948) (1)
- Extremal polynomials and the zeros of the derivative of a rational function (1964) (1)
- An Expansion of Meromorphic Functions. (1932) (1)
- The Circles of Curvature of the Curves of Steepest Descent of Green's Function (1961) (1)
- On Rouché’s theorem and the integral-square measure of approximation (1951) (1)
- On the degree of convergence of sequences of rational functions (1940) (1)
- Note on the location of the critical points of a real rational function (1951) (1)
- Note on Cauchy's Integral Formula (1916) (1)
- SOME ASPECTS OF THE FERMAT PROBLEM ( THIRD PAPER ) (1)
- Note on approximation by bounded analytic functions, problem α: General configurations (1968) (1)
- Approximation by rational functions on Riemann surfaces (1972) (1)
- Note on approximation by bounded analytic functions (Problem α) (1959) (1)
- Note on the degree of convergence of sequences of polynomials (1947) (0)
- A Paradox Resulting from Integration by Parts (1927) (0)
- On the Location of the Roots of Lamé's Polynomials (0)
- Note on approximation by bounded analytic functions, problem α: General configurations (1968) (0)
- Approximation by bounded analytic functions to functions represented by Dirichlet series (1961) (0)
- Some two-dimensional loci connected with cross ratios (0)
- Bateman on Mathematical Physics (1933) (0)
- Approximation by polynomials: uniform convergence as implied by mean convergence, ii. (1966) (0)
- On the asymptotic properties of extremal polynomials with prescribed constant term (1960) (0)
- The location of the critical points of simply and doubly periodic functions (1947) (0)
- The role of the pole in rational approximation (1974) (0)
- Methods of Symmetry and Critical Points of Harmonic Functions. (1948) (0)
- A rigorous treatment of maximum-minimum problems in the calculus (1962) (0)
- DEGREE OF APPROXIMATION BY BOUNDED HARMONIC FUNCTIONS. (1960) (0)
- Note on degree of approximation by bounded analytic functions: Problem (1960) (0)
- A necessary condition for approximation by rational functions (1936) (0)
- On the growth of derivatives of functions omitting two values (1949) (0)
- On the proof of Cauchy’s integral formula by means of Green’s formula (0)
- Approximation by bounded analytic functions: Uniform convergence as implied by mean convergence (1968) (0)
- On the Degree of Convergence of Harmonic Polynomials to Harmonic Functions. (1949) (0)
- THE DEGREE OF CONVERGENCE OF SEQUENCES OF LINEAR POSITIVE OPERATORS (0)
- On the location of the zeros of certain orthogonal functions (1956) (0)
- Some Interpolation Series (1934) (0)
- Questions and Discussions (1927) (0)
- A generalization of evolutes (1924) (0)
- Note on the Critical Points of Harmonic Functions. (1947) (0)
- Note on the location of the critical points of harmonic functions (1946) (0)
- THE FACTORIZATION OF CYCLIC REDUCED POWERS BY SECONDARY COHOMOLOGY OPERATIONS (0)
- RESTRICTED INFRAPOLYNOMIALS AND TRIGONOMETRIC INFRAPOLYNOMIALS. (1963) (0)
- Note on degree of convergence of sequences of rational functions of prescribed type. (1970) (0)
- Note on the Behavior of a Polynomial at Infinity (1936) (0)
- Best approximation by rational functions and by meromorphic functions with some free poles (1967) (0)
- On the shape of the level loci of harmonic measure (1970) (0)
- A PERSISTENT LOCAL MAXIMUM OF THE pth POWER DEVIATION ON AN INTERVAL, p < 1 (1968) (0)
- An Extremal Problem in Analytic Functions. (1933) (0)
- A theorem on loci connected with cross-ratios (1922) (0)
- CONFORMAL MAPS OF SMALL DISKS. (1961) (0)
- Note on overconvergence in sequences of analytic functions (1952) (0)
- Note on the Location of the Zeros of the Derivative of a Rational Function Having Prescribed Symmetry. (1946) (0)
- A generalization of Fejér’s principle concerning the zeros of extremal polynomials (1963) (0)
- On interpolation to an analytic function in equidistant points: problem $\beta$ (1949) (0)
- Asymptotic properties of polynomials with auxiliary conditions of interpolation (1962) (0)
- A generalization of normal congruences of circles (1922) (0)
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