Norman Levinson
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Most Influential Person Across History
American mathematician
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Mathematics
Why Is Norman Levinson Influential?
(Suggest an Edit or Addition)According to Wikipedia, Norman Levinson was an American mathematician. Some of his major contributions were in the study of Fourier transforms, complex analysis, non-linear differential equations, number theory, and signal processing. He worked closely with Norbert Wiener in his early career. He joined the faculty of the Massachusetts Institute of Technology in 1937. In 1954, he was awarded the Bôcher Memorial Prize of the American Mathematical Society and in 1971 the Chauvenet Prize of the Mathematical Association of America for his paper A Motivated Account of an Elementary Proof of the Prime Number Theorem. In 1974 he published a paper proving that more than a third of the zeros of the Riemann zeta function lie on the critical line, a result later improved to two fifths by Conrey.
Norman Levinson'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
- Theory of Ordinary Differential Equations (1955) (5311)
- The Wiener (Root Mean Square) Error Criterion in Filter Design and Prediction (1946) (1157)
- Gap and Density Theorems (1940) (567)
- A Second Order Differential Equation with Singular Solutions (1949) (267)
- The asymptotic nature of solutions of linear systems of differential equations (1948) (208)
- A general equation for relaxation oscillations (1942) (204)
- More than one third of zeros of Riemann's zeta-function are on σ = 12 (1974) (176)
- Transformation Theory of Non-Linear Differential Equations of the Second Order (1944) (150)
- A class of continuous linear programming problems (1966) (117)
- Zeros of the derivatives of the Riemann zeta-function (1974) (112)
- On the uniqueness of the potential in a Schrödinger equation for a given asymptotic phase (1949) (103)
- Linear programming in complex space (1966) (103)
- The First Boundary Value Problem for εΔu + A(x, y)u x + B(x, y)u y + C(x, y)u = D(x, y) for Small ε (1950) (97)
- Non-linear mechanics (1942) (94)
- Periodic Solutions of Singularly Perturbed Systems (1955) (94)
- A nonlinear Volterra equation arising in the theory of superfluidity (1960) (85)
- Generalization of an inequality of Ky Fan (1964) (78)
- Perturbations of discontinuous solutions of non-linear systems of differential equations (1947) (76)
- Generalizations of an inequality of Hardy (1964) (69)
- Singular Perturbations of Non-Linear Systems of Differential Equations and an Associated Boundary Layer Equation (1954) (68)
- Weighted trigonometrical approximation onR1 with application to the Germ field of a stationary Gaussian noise (1964) (68)
- On The Existence of Periodic Solutions For Second Order Differential Equations with a Forcing Term (1943) (62)
- Small Periodic Pertubations of an Autonomous System with a Stable Orbit (1950) (62)
- A simplified proof of the expansion theorem for singular second order linear differential equations (1951) (62)
- A boundary value problem for a nonlinear differential equation with a small parameter (1952) (59)
- The Asymptotic Behavior of a System of Linear Differential Equations (1946) (55)
- Ω-theorems for the Riemann zeta-function (1972) (50)
- A Heuristic Exposition of Wiener's Mathematical Theory of Prediction and Filtering (1947) (49)
- ON AN INEQUALITY OF OPIAL AND BEESACK (1964) (45)
- A boundary value problem for a singularly perturbed differential equation (1955) (35)
- CERTAIN EXPLICIT RELATIONSHIPS BETWEEN PHASE SHIFT AND SCATTERING POTENTIAL (1953) (34)
- Transformation of an analytic function of several variables to a canonical form (1961) (31)
- On a Class of Non‐Vanishing Functions (1936) (30)
- Criteria for the limit-point case for second order linear differential operators (1949) (30)
- Almost All Roots of zeta(s) = a Are Arbitrarily Close to sigma = 1/2. (1975) (30)
- On a Non-linear Differential Equation of the Second Order (1943) (27)
- Completeness and Independence of the Exponential Solutions of Some Functional Differential Equations (1974) (27)
- The growth of solutions of a differential equation (1942) (26)
- Positive eigenfunctions for Δu + λf(u) = 0 (1962) (23)
- Determination of the Potential from the Asymptotic Phase (1949) (22)
- Minimax, Liapunov and “bang-bang” (1966) (21)
- On the Asymptotic Shape of the Cavity Behind an Axially Symmetric Nose Moving Through an Ideal Fluid [1] (1946) (20)
- A Motivated Account of an Elementary Proof of the Prime Number Theorem (1969) (20)
- Limiting theorems for Galton-Watson branching process (1959) (18)
- A polynomial canonical form for certain analytic functions of two variables at a critical point (1960) (17)
- Limiting theorems for age-dependent branching processes (1960) (17)
- Emission Probability in a Random Walk (1962) (17)
- The Gontcharoff polynomials (1944) (16)
- A canonical form for an analytic function of several variables at a critical point (1960) (16)
- Deduction of Semi-Optimal Mollifier for Obtaining Lower Bound for N(0)(T) for Riemann's Zeta-Function. (1975) (16)
- On the non-uniqueness of periodic solutions for an asymmetric Liénard equation (1952) (15)
- Simplified Treatment of Integrals of Cauchy Type, the Hilbert Problem and Singular Integral Equations. Appendix: Poincaré-Bertrand Formula (1965) (14)
- Review: V. V. Nemytskii and V. V. Stepanov, Qualitative theory of differential equations. Parts I and II (1961) (13)
- Zeros of derivative of Riemann's $\xi$-function (1974) (11)
- On the growth of analytic functions (1938) (11)
- The growth of the solutions of a differential equation (1941) (11)
- A Simple Second Order Differential Equation with Singular Motions. (1948) (11)
- Coding Theory: A Counterexample to G. H. Hardy's Conception of Applied Mathematics (1970) (10)
- On the Nature of the Spectrum of Singular Second Order Linear Differential Equations (1951) (10)
- On Non-Harmonic Fourier Series (1936) (10)
- On theorems of Berlowitz and Berndt (1971) (9)
- Asymptotic Behavior of Solutions of Non-linear Differential Equations (1969) (9)
- A theorem of Boas (1941) (9)
- Asymptotic Formula for the Coordinates of the Zeros of Sections of the Zeta Function, zeta(N)(s), Near s = 1. (1973) (8)
- Selected papers of Norbert Wiener, including Generalized harmonic analysis and Tauberian theorems (1964) (7)
- Forced Periodic Solutions of a Stable Non-Linear System of Differential Equations (1950) (7)
- Remarks on a formula of Riemann for his zeta-function (1973) (6)
- On stability of non-linear systems of differential equations (1949) (6)
- At Least One-Third of Zeros of Riemann's Zeta-Function are on sigma = (1/2). (1974) (6)
- THE EXPANSION THEOREM FOR SINGULAR SELF-ADJOINT LINEAR DIFFERENTIAL OPERATORS* (1954) (6)
- Correction: Transformation Theory of Non-Linear Differential Equations of the Second Order (1948) (6)
- Gap and Density Theorems (Colloquium Publications (Amer Mathematical Soc)) (1940) (6)
- Gap and Density Theorems (Colloquium Publications) (1940) (6)
- On a Problem of Polya (1936) (5)
- On the Poisson summability of Fourier series (1936) (5)
- On the Szasz-Müntz theorem (1974) (5)
- On a Theorem of Carleman. (1934) (5)
- On closure problems and the zeros of the Riemann zeta function (1956) (4)
- Addendum to “A simplified proof of the expansion theorem for singular second order linear differential equations” (1951) (4)
- On the Elementary Proof of the Prime Number Theorem (1966) (4)
- A simplification in the proof that N0(T) > (13)N(T) for Riemann's zeta-function (1975) (4)
- The stability of linear, real, periodic self-adjoint systems of differential equations (1963) (4)
- On the elementary character of Wiener's general Tauberian theorem (1973) (4)
- Summing certain number theoretic series arising in the sieve (1968) (4)
- A Theorem Relating Non-vanishing and Analytic Functions (1937) (4)
- General Gap Tauberian Theorems: I (1938) (4)
- The Prime Number Theorem from logn (1964) (3)
- Transform and inverse transform expansions for singular self-adjoint differential operators (1958) (3)
- Corrections to “The Gontcharoff polynomials” (1945) (3)
- On the Closure of and Integral Functions (1935) (3)
- An Ordinary Differential Equation with an Interval of Stability, A Separation Point, and an Interval of Instability (1949) (3)
- An Integral Inequality of the Phragmen Lindelof Type (1941) (3)
- omega-Theorems for Quotients of Zeta-Functions at Combinations of Points. (1972) (2)
- The Fourier Transform Solution of Ordinary and Partial Differential Equations (1935) (2)
- Restrictions imposed by certain functions on their Fourier transforms (1940) (2)
- On the Non-Vanishing of Certain Functions. (1936) (2)
- On Ramakrishnan's approach to relativity (1974) (2)
- A Variant of the Selberg Inequality (1965) (2)
- POSITIVE EIGENFUNCTIONS FOR DELTA U+ LAMBDA F(U)=0, (1962) (2)
- II. Perturbations of Linear Systems with Constant Coefficients Possessing Periodic Solutions (1953) (2)
- The prime number theorem from (1964) (2)
- An Elementary Proof of the Stationary Distribution for an Irreducible Markov Chain (1965) (2)
- Remark about Wintner’s comparison theorem (1958) (1)
- Inequalities satisfied by a certain definite integral (1937) (1)
- Generalization of Recent Method Giving Lower Bound for N(o)(T) of Riemann's Zeta-Function. (1974) (1)
- One-sided inequalities for elliptic differential operators (1965) (1)
- On U + (1 + λg(x))u = 0 for ∞ 0 || g(x) || dx < ∞ (1959) (1)
- The sum of the intersections of a cone with a linear subspace and of dual cone with orthogonal complementary subspace (1966) (1)
- Zeros of the Riemann zeta-function near the 1-line☆ (1969) (1)
- Absolute convegence and the general high indices theorem (1964) (1)
- On the closure of $\{e^{i\lambda_nx}\}$ (1936) (1)
- On certain theorems of Pólya and Bernstein (1936) (1)
- Review: E. C. Titchmarsh, The theory of the Riemann zeta-function (1952) (1)
- On the closure of {^{_{}}}, II (1940) (1)
- On Certain Non-Linear Differential Equations of the Second Order. (1943) (1)
- On a Theorem of Ingham (1936) (1)
- A density theorem of Pólya (1940) (1)
- Zeros of entire functions of exponential type (1940) (0)
- The general higher indices theorem (1940) (0)
- Book Review: Fourier Series and Boundary Value Problems (1941) (0)
- Weighted trigonometrical approximation on $R^1$ with application to the germ field of a stationary Gaussian process (1964) (0)
- Recent contributions to the theory of random functions. (1946) (0)
- Existence of functions of zero type bounded on a sequence of points (1940) (0)
- On the secondary zeta-functions (1976) (0)
- Les Equations Differentielles de la Technique. (1949) (0)
- Book Review: The theory of the Riemann zeta-function (1952) (0)
- On restrictions necessary for certain higher indices theorems (1940) (0)
- On ”+(1+())=0 for ∫₀^{∞}\vert()\vert<∞ (1959) (0)
- Deduction of Semi-Optimal Mollifier for Obtaining Lower Bound for No ( T ) for Riemann ' s Zeta-Function ( Euler-Lagrange equation for mollifier ) (0)
- The general unrestricted Tauberian theorem for larger gaps (1940) (0)
- Fourier transforms of nonvanishing functions (1940) (0)
- Correction and addendum to “summing certain number theoretic series arising in the sieve” (1969) (0)
- Correction to "On Certain Non-Linear Differential Equations of the Second Order" (1943) (0)
- On Hardy's Theorem on the Zeros of the Zeta Function (1940) (0)
- DIRICHLET PROBLEM FOR DELTA U = F (P,U), (1962) (0)
- On $u”+(1+\lambda g(x))u=0$ for $\int \sb{0}{}\sp{\infty }\,\vert g(x)\vert dx<\infty $ (1959) (0)
- Schur’s Theorem for Hurwitz Polynomials (1972) (0)
- Ω-Theorems for the real part of the Riemann zeta function (1973) (0)
- An inequality and functions of zero type (1940) (0)
- Review: R. V. Churchill, Fourier Series and Boundary Value Problems (1941) (0)
- Functional Analysis . Frigyes Fiesz and Bela Sz.-Nagy. Translated from the French ed. 2 by Leo F. Boron. Ungar, New York, 1955. 468 pp. $10. (1956) (0)
- Determination of the rate of growth of analytic functions from their growth on sequences of points (1940) (0)
- Integral functions bounded on sequences of points (1938) (0)
- The $\mathcal{L}$-closure of eigenfunctions associated with self-adjoint boundary value problems (1952) (0)
- omega-Theorems for Riemann's Zeta-Function at Harmonic Combinations of Points. (1972) (0)
- Recent Contributions to the Theory of Random Functions. (1946) (0)
- Ethics of Lobotomies (1972) (0)
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