Ralph P. Boas Jr.
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American mathematician
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Mathematics
Why Is Ralph P. Boas Jr. Influential?
(Suggest an Edit or Addition)According to Wikipedia, Ralph Philip Boas Jr. was a mathematician, teacher, and journal editor. He wrote over 200 papers, mainly in the fields of real and complex analysis. Biography He was born in Walla Walla, Washington, the son of an English professor at Whitman College, but moved frequently as a child; his younger sister, Marie Boas Hall, later to become a historian of science, was born in Springfield, Massachusetts, where his father had become a high school teacher. He was home-schooled until the age of eight, began his formal schooling in the sixth grade, and graduated from high school while still only 15. After a gap year auditing classes at Mount Holyoke College he entered Harvard, intending to major in chemistry and go into medicine, but ended up studying mathematics instead. His first mathematics publication was written as an undergraduate, after he discovered an incorrect proof in another paper. He got his A.B. degree in 1933, received a Sheldon Fellowship for a year of travel, and returned to Harvard for his doctoral studies in 1934. He earned his doctorate there in 1937, under the supervision of David Widder.
Ralph P. Boas Jr.'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
- Polynomial Expansions of Analytic Functions (1958) (279)
- Integrability theorems for trigonometric transforms (1967) (149)
- The Stieltjes moment problem for functions of bounded variation (1939) (96)
- Higher Transcendental Functions, vols. I and II.Based, in part, on notes left by Harry Bateman.Bateman Project Staff, A. Erdélyi, Ed. McGraw-Hill, New York-London, 1953. vol. I, xxvi + 302 pp.,$6.50; vol. II, xviii + 396 pp., $7.50 (1954) (76)
- Inequalities for Fourier transforms of positive functions (1945) (75)
- Fourier series with positive coefficients (1966) (63)
- Quasi‐Positive Sequences and Trigonometric Series† (1965) (59)
- A General Moment Problem (1941) (56)
- SUMMATION FORMULAS AND BAND-LIMITED SIGNALS (1972) (53)
- Some uniformly convex spaces (1940) (52)
- Partial Sums of Infinite Series, and How They Grow (1977) (48)
- Integrability of trigonometric series. I. (1951) (40)
- Functions with positive differences (1940) (39)
- Some integral inequalities related to Hardy's inequality (1970) (38)
- Representation of functions by Lidstone series (1943) (36)
- Inequalities for the Derivatives of Polynomials (1969) (35)
- On a Theorem of M. Riesz for Fourier Series (1939) (29)
- Majorant problems for trigonometric series (1962) (28)
- A New Use for an Old Counterexample (1975) (27)
- A New Use for an Old Counterexample (1975) (27)
- Complete Sets of Bessel and Legendre Functions (1947) (26)
- Lp inequalities for polynomials and entire functions (1962) (26)
- The growth of solutions of a differential equation (1942) (26)
- Lipschitz Behavior and Integrability of Characteristic Functions (1967) (25)
- Some theorems on Fourier transforms and conjugate trigonometric integrals (1936) (25)
- Tables of Integral Transforms, vol. I. Based, in part, on notes left by Harry Bateman. Bateman Project Staff, A. Erdélyi, Ed. McGraw-Hill, New York— London, 1954. xx + 391 pp. $7.50 (1954) (25)
- Polynomial Expansions of Analytic Functions. (1959) (25)
- Absolute Convergence and Integrability of Trigonometric Series (1956) (25)
- Inequalities for asymmetric entire functions (1957) (24)
- A uniqueness theorem for harmonic functions (1972) (24)
- INTEGRABILITY OF TRIGONOMETRIC SERIES (III) (1952) (23)
- Partial Differential Equations: An Introduction to a General Theory of Linear Boundary Value Problems (1987) (22)
- The integrability class of the sine transform of a monotonic function (1972) (22)
- Polynomials Defined by Generating Relations (1956) (21)
- Extremal Problems for Polynomials (1978) (21)
- The multiplicative completion of sets of functions (1948) (21)
- Expansions of analytic functions (1940) (20)
- Signs of Derivatives and Analytic Behavior (1971) (20)
- Can We Make Mathematics Intelligible (1981) (19)
- The Derivative of a Trigonometric Integral (1937) (19)
- Continuous Analogues of Series (1973) (19)
- Isomorphism Between H p and L p (1955) (18)
- Estimating Sums with Integrals (1971) (17)
- A note on functions of exponential type (1941) (17)
- Entire functions bounded on a line (1940) (16)
- Representations for Entire Functions of Exponential Type (1938) (16)
- Inverse Functions and Integration by Parts (1974) (16)
- Beurling's test for absolute convergence of Fourier series (1960) (16)
- Inequalities for monotonic series (1960) (15)
- Functions of exponential type, II (1944) (14)
- Littlewood's Miscellany. Edited by Béla Bollobás (1989) (14)
- Elementary Convolution Inequalities (1975) (13)
- Generalizations of Young's inequality (1974) (13)
- Univalent derivatives of entire functions (1940) (13)
- Growth of partial sums of divergent series (1977) (13)
- Asymptotic relations for derivatives (1937) (13)
- A class of gap theorems (1948) (13)
- Inequalities Involving a Function and Its Inverse (1973) (13)
- Short proofs of three theorems on harmonic functions (1988) (13)
- Representation of Probability Distributions by Charlier Series (1949) (13)
- A theorem on analytic functions of a real variable (1935) (13)
- The iterated Stieltjes transform (1939) (12)
- Growth of analytic functions along a line (1952) (12)
- Tannery's Theorem (1965) (12)
- Integrability along a line for a class of entire functions (1952) (12)
- Partial Sums of the Harmonic Series (1971) (12)
- An inversion formula for the Laplace integral (1940) (11)
- Entire functions of exponential type (1942) (10)
- Partial Sums of Fourier Series. (1951) (10)
- Variational Methods in Entire Functions (1957) (10)
- Yet Another Proof of the Fundamental Theorem of Algebra (1964) (10)
- Generalized Laplace integrals (1942) (10)
- Counterexamples to L'Hoˆpital's rule (1986) (9)
- Influence of the signs of the derivatives of a function on its analytic character (1942) (9)
- A Completeness Theorem (1940) (9)
- SOME INTEGRABILITY THEOREMS FOR POWER SERIES WITH POSITIVE COEFFICIENTS. (1968) (9)
- A theorem of Cartwright (1942) (9)
- Basic sets of polynomials. II (1948) (8)
- Functions with positive derivatives (1941) (8)
- More About Quotients of Monotone Functions (1965) (8)
- More inequalities for Fourier transforms (1948) (8)
- Indefinite Integration by Residues (1966) (8)
- Multivariate Pad&Approximants* (1983) (8)
- Lhospital's Rule Without Mean-Value Theorems (1969) (8)
- Asymptotic properties of functions of exponential type (1953) (8)
- Fundamental Sets of Entire Functions (1946) (7)
- The asymptotic behavior of inhomogeneous means (1987) (7)
- Who Needs Those Mean-Value Theorems, Anyway? (1981) (7)
- Some Uniqueness Theorems for Entire Functions (1940) (7)
- Representations for Completely Convex Functions (1959) (7)
- Remarks on a moment problem (1953) (7)
- Integral Functions With Negative Zeros (1953) (7)
- Density theorems for power series and complete sets (1947) (7)
- A Tauberian Theorem Connected with the Problem of Three Bodies (1939) (7)
- Inequalities for functions of exponential type (1956) (6)
- When is a C∞ function analytic? (1989) (6)
- Correction for "Indefinite Integration by Residues" (1964) (6)
- Properties equivalent to the completeness of $\left\{ {e^{ - t} t^{\lambda _n } } \right\}$ (1946) (6)
- Sums representing Fourier transforms (1952) (6)
- Lion Hunting and Other Mathematical Pursuits. (1996) (5)
- Poisson's Summation Formula in L2 (1946) (5)
- Review: Peter Henrici, Applied and computational complex analysis (1975) (5)
- Indeterminate forms revisited (1990) (5)
- Some elementary theorems on entire functions (1952) (5)
- A Proof of the Fundamental Theorem of Algebra (1935) (5)
- New Inequalities for Entire Functions (1958) (5)
- INTEGRABILITY OF NONNEGATIVE TRIGONOMETRIC SERIES (1962) (4)
- A note on linear functionals (1938) (4)
- A Primer of Real Functions. (1961) (4)
- Review: N. G. de Bruijn, Asymptotic methods in analysis (1959) (4)
- Integrability Theorems for Laplace‐Stieltjes Transforms* (1957) (4)
- Lion hunting & other mathematical pursuits : a collection of mathematics, verse, and stories (1995) (4)
- On the Characterization of a Distribution Function by Its Fourier Transform (1938) (4)
- Forecasting under unstable conditions: A case study of the cocoa market (1989) (4)
- The atypical zeros of a class of entire functions (1964) (4)
- Integrability of non-negative trigonometric series, II (1964) (4)
- Tauberian theorems for $(C,1)$ summability (1938) (4)
- Fourier coefficients of positive functions (1967) (4)
- The Asymptotic Behavior of Derivatives (1978) (4)
- Generalization of Completely Convex Functions. (1941) (4)
- An extension of Carlson's theorem for analytic functions (1988) (3)
- On a generalization of the Stieltjes moment problem (1939) (3)
- Higher Transcendental Functions . vol. III. Based in part on notes left by Harry Bateman. Bateman Project Staff, A. Erdélyi, Ed. McGraw-Hill, New York-London, 1955. xviii + 292 pp. $6.50. (1955) (3)
- Extrema of Polynomials (1977) (3)
- Review: J. R. Higgins, Completeness and basis properties of sets of special functions (1978) (3)
- A Trigonometric Moment Problem (1939) (3)
- Award for Distinguished Service to Otto Neugebauer (1979) (3)
- Advanced Problems: 6415-6420 (1983) (3)
- Calculus as an Experimental Science. (1971) (3)
- Integrability of trigonometric series. II (1952) (3)
- Interference phenomena for entire functions. (1955) (3)
- Inversion of a Generalized Laplace Integral. (1942) (3)
- On Generalized Averaging Operators (1958) (3)
- The growth of analytic functions (1946) (3)
- If This Be Treason (1957) (3)
- Level sets of derivatives. (1979) (2)
- Some gap theorems for power series (1938) (2)
- Indefinite Integration by Residues II (1964) (2)
- Addendum: Derivatives of infinite order (1951) (2)
- Zeros of the successive derivatives of entire functions (1973) (2)
- A constant in the theory of trigonometric series (1964) (2)
- Review: Emil Grosswald, Bessel polynomials (1979) (2)
- Singularities of analytic functions (1974) (2)
- Review: A. M. Olevskiĭ, Fourier series with respect to general orthogonal systems (1976) (2)
- Inversion of Fourier and Laplace Transforms (1962) (2)
- Inequalities for a Collection (1979) (2)
- Distribution of Digits in Integers (1977) (2)
- Selected Topics from Pólya's Work in Complex Analysis (1987) (2)
- A variational method for trigonometric polynomials (1959) (2)
- Review: Gustav Doetsch, Handbuch der Laplace-Transformation, Vol. II. Anwendungen der Laplace-Transformation. Part 1 (1956) (2)
- General Expansion Theorems. (1940) (2)
- Derivatives of infinite order (1948) (2)
- Closure Theorems for Translations (1938) (2)
- Growth of derivatives of entire functions (1957) (1)
- Periodic Entire Functions (1964) (1)
- Zeros of successive derivatives of entire functions (1973) (1)
- Problems for Solution: 4270,4728-4732 (1957) (1)
- Award for Distinguished Service to Professor Saunders Mac Lane (1975) (1)
- The Charlier $B$-series (1949) (1)
- Correction: Derivatives of infinite order (1948) (1)
- The Cosrims Reports (1970) (1)
- Necessary and sufficient conditions in the moment problem for a finite interval (1935) (1)
- A series considered by Ramanujan (1960) (1)
- Oscillation of partial sums of Fourier series (1952) (1)
- Exponential Transforms and Appell Polynomials. (1948) (1)
- Old intelligencer (1986) (1)
- The Set on Which an Entire Function is Small (1948) (1)
- Simplification of Some Contour Integrations (1985) (1)
- Elementary Problems: E2830-E2834 (1980) (1)
- An Integral Test for Convergence (1949) (1)
- A remark on principal-value integrals (1984) (1)
- On sine series with positive coefficients (1962) (1)
- Two Theorems on Integral Functions (1953) (1)
- Differentiability of jump functions (1961) (0)
- assuming abscissa of convergence uC to be zero, and their Stieltjes transforms (1982) (0)
- Moments of analytic functions (1955) (0)
- 2252. Convergence of series and integrals (1951) (0)
- 3. Shakespeare’s the Tempest, V, i, 181-184 Miranda’s Speech inthe Tempest (1943) (0)
- Mathematics: Elementary Theory of Analytic Functions of One or Several Complex Variables . Henri Cartan. Translated from the French edition. Hermann, Paris; Addison-Wesley, Reading, Mass., 1963. 228 pp. Illus. $10.75. (1964) (0)
- Selecta: Expository Writing. By P. R. Halmos (1985) (0)
- Problems for Solution: 5101-5110 (1963) (0)
- Intermediate Real Analysis (Emanuel Fischer) (1984) (0)
- A Density Theorem for Power Series (1946) (0)
- Correction to “Entire functions bounded on a line” (1946) (0)
- Completeness of sets of translated cosines (1951) (0)
- Multiplying Long Numbers (1989) (0)
- A correction to “A note on linear functionals” (1940) (0)
- A Primer of Real Functions: Sets (1996) (0)
- Book Review: Journal d'Analyse Mathématique. (1954) (0)
- Asymptotic formulas and Lipschitz conditions (1967) (0)
- More general classes of functions; conditional convergence (1967) (0)
- A Tauberian theorem for integral functions (1953) (0)
- Shorter Notes: An Inequality for Nonnegative Entire Functions (1962) (0)
- Capitalizaton of language references (1966) (0)
- 35. Housman’s Revolution (LP36) (1944) (0)
- Representation of functions that are regular at the origin (1958) (0)
- Theorems with positive or decreasing coefficients (1967) (0)
- Theorems with positive or decreasing functions (1967) (0)
- Armed with Integration... (1982) (0)
- Review: T. W. Chaundy and P. R. Barrett and Charles Batey, The printing of mathematics. Aids for authors and editors and rules for compositors and readers at the University Press, Oxford, and , Mathematics in type (1955) (0)
- Elementary Problems: E2719-E2724 (1978) (0)
- Review: I. P. Natanson, Konstruktive Funktionentheorie (1956) (0)
- Nevertheless, Let's Get on with the Job (1981) (0)
- A Primer of Real Functions: Functions (1996) (0)
- Review: Norman Levinson, Gap and Density Theorems (1941) (0)
- Explaining the Line of Position (1954) (0)
- Letter to an Author (1980) (0)
- Review: Leo Herland, Dictionary of mathematical sciences Vol. 1 (1952) (0)
- Book Review: The printing of mathematics. Aids for authors and editors and rules for compositors and readers at the University Press, Oxford@@@Book Review: Mathematics in type (1955) (0)
- An inequality for nonnegative entire functions (1962) (0)
- Review: Henry Margenau and George Moseley Murphy, The mathematics of physics and chemistry (1959) (0)
- Are Mathematicians Unnecessary? (1980) (0)
- Fifty Years Ago (1952) (0)
- 29. Shakespeare’s Twelfth Night, II, iii, 25-27 (1945) (0)
- 29. Shakespeare’s Twelfth Night, II, iii, 25-27 (1945) (0)
- Infinite Processes: Background to Analysis. By A. Gardiner (1983) (0)
- Book reviewQuantitative forecasting methods: N.R. FARNUM and L.W. STANTON Chapman and Hall, London, 1989, viii + 573 pages, £18.95 (1990) (0)
- Early Days at Mathematical Reviews (1991) (0)
- Generalized Taylor Series, Quadrature Formulas, and a Formula by Kronecker (1970) (0)
- Inequalities for monotonic entire functions. (1963) (0)
- Almost completely convex functions (1958) (0)
- An upper bound for the Gontcharoff constant (1948) (0)
- A Treatise on Trigonometric Series (N. K. Bary) (1965) (0)
- Problems for Solution: E771-E775 (1947) (0)
- Snowfalls and Elephants, Pop Bottles and Pi. (1980) (0)
- Review: James R. Newman, The world of mathematics (1957) (0)
- Names of Functions: The Problems of Trying for Precision (1983) (0)
- Review: D. V. Widder, The heat equation (1976) (0)
- Book Review: Michigan Mathematical Journal (1954) (0)
- Advanced Problems: 5922-5927 (1973) (0)
- Elementary Problems: E2671-E2676 (1977) (0)
- Order of magnitude of Fourier transforms. (1953) (0)
- 62.34 Means derived from convergent series (1978) (0)
- Retroactive Editorial Policy (1982) (0)
- Power Series for Practical Purposes (1982) (0)
- A differential inequality (1945) (0)
- THE ATYPICAL OF A CLASS OF ENTIRE FUNCTIONS (1963) (0)
- The exceptional integral values of the index (1967) (0)
- Review: C. Hastings, Jr., Approximations for digital computers (1955) (0)
- Problems for Solution: 4415-4419 (1950) (0)
- Quantitative forecasting methods (1990) (0)
- The Rate of Growth of Analytic Functions. (1946) (0)
- Elementary Problems: E2932-E2937 (1982) (0)
- Jazz, Literature, and the Teaching of Mathematics (1979) (0)
- Does “holds water” Hold Water? (1986) (0)
- Representation of entire functions (1958) (0)
- Probability, Precipitation and π (1980) (0)
- Book Review: Contributions to the founding of the theory of transfinite numbers@@@Book Review: A philosophical essay on probabilities (1952) (0)
- Comment on “Kinematics Problem for Joggers” (1974) (0)
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