Selected papers of Norman Levinson

著者

• Levinson, Norman
• Nohel, John A.
• Sattinger, David H.

書誌事項

Selected papers of Norman Levinson

John A. Nohel, David H. Sattinger, editors

（Contemporary mathematicians）

Birkhäuser, c1998

• : set : Boston
• : set : Basel
• v. 1 : Boston
• v. 1 : Basel
• v. 2 : Boston
• v. 2 : Basel

注記

Includes bibliographical references

内容説明・目次

巻冊次

v. 1 : Boston ISBN 9780817638627

内容説明

The deep and original ideas of Norman Levinson have had a lasting impact on fields as diverse as differential & integral equations, harmonic, complex & stochas tic analysis, and analytic number theory during more than half a century. Yet, the extent of his contributions has not always been fully recognized in the mathematics community. For example, the horseshoe mapping constructed by Stephen Smale in 1960 played a central role in the development of the modern theory of dynami cal systems and chaos. The horseshoe map was directly stimulated by Levinson's research on forced periodic oscillations of the Van der Pol oscillator, and specifi cally by his seminal work initiated by Cartwright and Littlewood. In other topics, Levinson provided the foundation for a rigorous theory of singularly perturbed dif ferential equations. He also made fundamental contributions to inverse scattering theory by showing the connection between scattering data and spectral data, thus relating the famous Gel'fand-Levitan method to the inverse scattering problem for the Schrodinger equation. He was the first to analyze and make explicit use of wave functions, now widely known as the Jost functions. Near the end of his life, Levinson returned to research in analytic number theory and made profound progress on the resolution of the Riemann Hypothesis. Levinson's papers are typically tightly crafted and masterpieces of brevity and clarity. It is our hope that the publication of these selected papers will bring his mathematical ideas to the attention of the larger mathematical community.

目次

- Volume 1.- I. Stability and Asymptotic Behavior of Solutions of Ordinary Differential Equations.- Commentary on [L 31] and [L 36].- [L 20] The Growth of the Solutions of a Differential Equation (1941).- [L 24] The Growth of the Solutions of a Differential Equation (1942).- [L 31] The Asymptotic Behavior of a System of Linear Differential Equations (1946).- [L 36] The Asymptotic Nature of Solutions of Linear Systems of Differential Equations (1948).- [L 40] On Stability of Non-Linear Systems of Differential Equations (1949).- [L 68] On u? + (1 + ? g(x)) u = 0 for ?0? | g(x)|dx < ? (1959).- II. Nonlinear Oscillations and Dynamical Systems.- Commentary on [L 29], [L 38] and [L 47].- [L 23] A General Equation for Relaxation Oscillations (1942).- [L 25] On the Existence of Periodic Solutions for Second Order Differential Equations with a Forcing Term (1943).- [L 29] Transformation Theory of Non-Linear Differential Equations of the Second Order (1944) and Correction (1948).- [L 38] A Second Order Differential Equation with Singular Solutions (1949).- [L 47] Small Periodic Perturbations of an Autonomous System with a Stable Orbit (1950).- [L 52] Forced Periodic Solutions of a Stable Non-Linear System of Differential Equations (1951).- [L 57] On the Non-Uniqueness of Periodic Solutions for an Asymmetric Lienard Equation (1952).- III. Inverse Problems for Sturm-Liouville and Schroedinger Operators.- Commentary on [L 41], [L 43] and [L 58].- [L 41] On the Uniqueness of the Potential in a Schroedinger Equation for a Given Asymptotic Phase (1949).- [L 42] Determination of the Potential from the Asymptotic Phase (1949).- [L 43] The Inverse Sturm-Liouville Problem (1949).- [L 58] Certain Explicit Relationships between Phase Shift and Scattering Potential (1953).- IV. Eigenfunction Expansions and Spectral Theory for Ordinary Differential Equations.- Commentary on [L 49], [L 51], and [L 59].- [L 39] Criteria for the Limit-Point Case for Second Order Linear Differential Operators (1949).- [L 49] A Simplified Proof of the Expansions Theorem for Singular Second Order Linear Differential Equations (1951).- [L 50] Addendum to "A Simplified Proof of the Expansions Theorem for Singular Second Order Linear Differential Equations" (1951).- [L 51] On the Nature of the Spectrum of Singular Second Order Linear Differential Equations (1951).- [L 53] The L-Closure of Eigenfunctions Associated with Selfadjoint Boundary Value Problems (1952).- [L 59] The Expansion Theorem for Singular Self-Adjoint Linear Differential Operators (1954).- [L 65] Transform and Inverse Transform Expansions for Singular Self-Adjoint Differential Operators (1958).- V. Singular Perturbations of Ordinary and Partial Differential Equations.- Commentary on [L 45], [L 48], [L 60], [L 62], [L 63], [L 67], [L 56] and [L 46].- [L 45] Perturbations of Discontinuous Solutions of Non-Linear Systems of Differential Equations (1950).- [L 48] An Ordinary Differential Equation with an Interval of Stability, a Separation Point, and an Interval of Instability (1950).- [L 60] Singular Perturbations of Non-Linear Systems of Differential Equations and an Associated Boundary Layer Equation (1954).- [L 62] Periodic Solutions of Singularly Perturbed Systems (1955).- [L 56] A Boundary Value Problem for a Nonlinear Differential Equation with a Small Parameter (1952).- [L 63] A Boundary Value Problem for a Singularly Perturbed Differential Equation (1955).- [L 67] A Boundary Value Problem for a Singularly Perturbed Differential Equation (1958).- [L 46] The First Boundary Value Problem for ??u +A(x,y)ux + B(x,y)uy + C(x, y)u = D(x,y) for small ? (1950).- VI. Elliptic Partial Differential Equations.- Commentary on [L 75], [L 78], [L87].- [L 75] Positive Eigenfunctions for ?u + ?f(u) = 0 (1962).- [L 78] Dirichlet Problem for ?u = f(P, u) (1963).- [L 87] One-Sided Inequalities for Elliptic Differential Operators (1965).- VII. Integral Equations.- Commentary on [L 73].- [L 32] On the Asymptotic Shape of the Cavity Behind an Axially Symmetric Nose Moving Through an Ideal Fluid (1946).- [L 73] A Nonlinear Volterra Equation Arising in the Theory of Superfluidity (1960).- [L 89] Simplified Treatment of Integrals of Cauchy Type, the Hilbert Problem and Singular Integral Equations. Appendix: Poincar e-Bertrand Formula (1965).

巻冊次

: set : Boston ISBN 9780817639785

内容説明

The deep and original ideas of Norman Levinson have had a lasting impact on fields as diverse as differential & integral equations, harmonic, complex & stochas tic analysis, and analytic number theory during more than half a century. Yet, the extent of his contributions has not always been fully recognized in the mathematics community. For example, the horseshoe mapping constructed by Stephen Smale in 1960 played a central role in the development of the modern theory of dynami cal systems and chaos. The horseshoe map was directly stimulated by Levinson's research on forced periodic oscillations of the Van der Pol oscillator, and specifi cally by his seminal work initiated by Cartwright and Littlewood. In other topics, Levinson provided the foundation for a rigorous theory of singularly perturbed dif ferential equations. He also made fundamental contributions to inverse scattering theory by showing the connection between scattering data and spectral data, thus relating the famous Gel'fand-Levitan method to the inverse scattering problem for the Schrodinger equation. He was the first to analyze and make explicit use of wave functions, now widely known as the Jost functions. Near the end of his life, Levinson returned to research in analytic number theory and made profound progress on the resolution of the Riemann Hypothesis. Levinson's papers are typically tightly crafted and masterpieces of brevity and clarity. It is our hope that the publication of these selected papers will bring his mathematical ideas to the attention of the larger mathematical community.

目次

- Volume 1.- I. Stability and Asymptotic Behavior of Solutions of Ordinary Differential Equations.- Commentary on [L 31] and [L 36].- [L 20] The Growth of the Solutions of a Differential Equation (1941).- [L 24] (with Mary L. Boas and R. P. Boas, Jr.), The Growth of the Solutions of a Differential Equation (1942).- [L 31] The Asymptotic Behavior of a System of Linear Differential Equations (1946).- [L 36] The Asymptotic Nature of Solutions of Linear Systems of Differential Equations (1948).- [L 40] On Stability of Non-Linear Systems of Differential Equations (1949).- [L 68] (with R. R. D. Kemp), On $$u\prime \prime + \left( {1 + \lambda g\left( x \right)} \right)u = 0$$ for $$\int_0^\infty {\left| {g\left( x \right)} \right|dx} (1949).- [L 42] Determination of the Potential from the Asymptotic Phase (1949).- [L 43] The Inverse Sturm-Liouville Problem (1949).- [L 58] Certain Explicit Relationships between Phase Shift and Scattering Potential (1953).- IV. Eigenfunction Expansions and Spectral Theory for Ordinary Differential Equations.- Commentary on [L 49], [L 51], and [L 59].- [L 39] Criteria for the Limit-Point Case for Second Order Linear Differential Operators (1949).- [L 49] A Simplified Proof of the Expansions Theorem for Singular Second Order Linear Differential Equations (1951).- [L 50] Addendum to "A Simplified Proof of the Expansions Theorem for Singular Second Order Linear Differential Equations" (1951).- [L 51] (with E. A. Coddington), On the Nature of the Spectrum of Singular Second Order Linear Differential Equations (1951).- [L 53] TheL-Closure of Eigenfunctions Associated with Selfadjoint Boundary Value Problems (1952).- [L 59] The Expansion Theorem for Singular Self-Adjoint Linear Differential Operators (1954).- [L 65] Transform and Inverse Transform Expansions for Singular Self-Adjoint Differential Operators (1958).- V. Singular Perturbations of Ordinary and Partial Differential Equations.- Commentary on [L 45], [L 48], [L 60], [L 62], [L 63], [L 67], [L 56] and [L 46].- [L 45] Perturbations of Discontinuous Solutions of Non-Linear Systems of Differential Equations (1950).- [L 48] An Ordinary Differential Equation with an Interval of Stability, a Separation Point, and an Interval of Instability (1950).- [L 60] (with J. J. Levin), Singular Perturbations of Non-Linear Systems of Differential Equations and an Associated Boundary Layer Equation (1954).- [L 62] (with L. Flatto), Periodic Solutions of Singularly Perturbed Systems (1955).- [L 56] (with E. A. Coddington), A Boundary Value Problem for a Nonlinear Differential Equation with a Small Parameter (1952).- [L 63] (with S. Haber), A Boundary Value Problem for a Singularly Perturbed Differential Equation (1955).- [L 67] A Boundary Value Problem for a Singularly Perturbed Differential Equation (1958).- [L 46] The First Boundary Value Problem for$$ \in \Delta + {\rm A}\left( {x,y} \right){u_x} + {\rm B}\left( {x,y} \right){u_y} + C\left( {x,y} \right)u = D\left( {x,y} \right)$$ for small ? (1950).- VI. Elliptic Partial Differential Equations.- Commentary on [L 75], [L 78], [L 87].- [L 75] Positive Eigenfunctions for $$\Delta u + \lambda f\left( u \right) = 0$$ (1962).- [L 78] Dirichlet Problem for $$\Delta u = f\left( {<!-- -->{\rm P},u} \right)$$ (1963).- [L 87] One-Sided Inequalities for Elliptic Differential Operators (1965).- VII. Integral Equations.- Commentary on [L 73].- [L 32] On the Asymptotic Shape of the Cavity Behind an Axially Symmetric Nose Moving Through an Ideal Fluid (1946).- [L 73] A Nonlinear Volterra Equation Arising in the Theory of Superfluidity (1960).- [L 89] Simplified Treatment of Integrals of Cauchy Type, the Hilbert Problem and Singular Integral Equations. Appendix: Poincare-Bertrand Formula (1965).

巻冊次

v. 2 : Boston ISBN 9780817639792

内容説明

Norman Levinson (1912-1975) was a mathematician of international repute. This collection of his selected papers bears witness to the profound influence Levinson had on research in mathematical analysis with applications to problems in science and technology. Levinson's originality is reflected in his fundamental contributions to complex, harmonic and stochastic equations, and to analytic number theory, where he continued to make significant advances toward resolving the Riemann hypothesis up to the end of his life. The two volumes are divided by topic, with commentary by some of those who have felt the impact of Levinson's legacy.

目次

- Volume 2.- VIII. Harmonic and Complex Analysis1.- Commentary on Gap and Density Theorems by Raymond Redheffer.- [L 8] On the Closure of $$\left\{ {<!-- -->{e^{i{\lambda _n}x}}} \right\}$$ (1936).- [L 7] On a Class of Non-Vanishing Functions (1936).- [L 9] On a Problem of Polya (1936).- [L 10] On Certain Theorems of Polya and Bernstein (1936).- [L 11] On Non-Harmonic Fourier Series (1936).- [L13] A Theorem Relating Non-Vanishing and Analytic Functions (1938).- [L 14] On the Growth of Analytic Functions (1938).- [L 15] General Gap Tauberian Theorems: I (1938).- [L 17] Restrictions Imposed by Certain Functions on Their Fourier Transforms (1940).- [L 74] Transformation of an Analytic Function of Several Variables to a Canonical Form (1961).- [L 82] Absolute Convergence and the General High Indices Theorem (1964).- [L 107] (with R. M. Redheffer) Schur's Theorem for Hurwitz Polynomials (1972).- [L 115] On the Szasz-Muntz Theorem (1974).- IX. Stochastic Analysis.- Commentary on [L 33], [L 34], [L 69], [L 70] and [L 81] by Mark Pinsky.- [L 33] The Wiener RMS (Root Mean Square) Error Criterion in Filter Design and Prediction (1947).- [L 34] A Heuristic Exposition of Wiener's Mathematical Theory of Prediction and Filtering (1947).- [L 69] Limiting Theorems for Galton-Watson Branching Process (1959).- [L 70] Limiting Theorems for Age-Dependent Branching Process (1960).- [L 81] (with H. P. McKean, Jr.) Weighted Trigonometrical Approximation on R1 with Application to the Germ Field of a Stationary Gaussian Noise (1964).- X. Elementary Number Theory and the Prime Number Theorem.- [L 98] A Motivated Account of an Elementary Proof of the Prime Number Theorem (1969).- [L 109] On the Elementary Character of Wiener's General Tauberian Theorem (1973).- XI. The Riemann Zeta-Function.- XI. 1 Zeros on the Critical Line.- Commentary on [L 112], [L 113], [L 116], [L 117], [L 118], [L 120], [L 121] by Brian Conrey.- [L 19] On Hardy's Theorem on Zeros of the Zeta Function (1940).- [L 64] On Closure Problems and the Zeros of the Riemann Zeta Function (1956).- [L 99] Zeros of the Riemann Zeta-Function near the 1-Line (1969).- [L 103] On Theorems of Berlowitz and Berndt (1971).- [L 112] More than One Third of Zeros of Riemann's Zeta-Function are on ? = 1/2 (1974).- [L 113] Zeros of Derivative of Riemann's ?-Function (1974).- Corrigendum (1975).- [L 116] At least One-Third of Zeros of Riemann's Zeta-Function are on ? = 1/2 (1974).- [L 117] Generalization of Recent Method Giving Lower Bound for N0(T) of Riemann's Zeta-Function (1974).- [L 118] (with H. L. Montgomery) Zeros of the Derivatives of the Riemann Zeta-Function (1974).- [L 120] A Simplification of the Proof that >N0(T) > (1/3)N(T) for Riemann's Zeta-Function (1975).- [L 121] Deduction of Semi-Optimal Mollifier for Obtaining Lower Bound for >N0(T) of Riemann's Zeta-Function (1975).- XI.2 Omega Results for the Riemann-Zeta Function.- Commentary on [L 104] by Brian Conrey.- [L 104]?-Theorems for the Riemann-Zeta Function (1972).- XI.3 Other Papers on the Riemann Zeta-Function.- [L 108] Remarks on a Formula of Riemann for his Zeta Function (1973).- [L 111] Asymptotic Formula for the Coordinates of the Zeros of Sections of the Zeta Function,?N (s), near s = 1 (1973).- [L 122] Almost All Roots of ?(s) = a Are Arbitrarily Close to ? = 1/2 (1975).- [L 123] On the Number of Sign Changes of ?(x)-li x (1976).- XII. Miscellaneous Topics.- Commentary on [L 91] by John Nohel and Hector Sussman.- Commentary on [L 114] by Alladi Ramakrishnan.- [L 12] (with G. H. Hardy), Inequalities Satisfied by a Certain Definite Integral (1937).- [L 79] Generalization of an Inequality of Ky Fan (1964).- [L 83] Generalizations of an Inequality of Hardy.- [L 91] Minimax, Liapunov and "Bang-Bang" (1966).- [L 92] Linear Programming in Complex Space (1966).- [L 93] A Class of Continuous Linear Programming Problems (1966).- [L 114] On Ramakrishnan's Approach to Relativity (1974).

巻冊次

v. 1 : Basel ISBN 9783764338626

内容説明

Norman Levinson (1912-1975) was a mathematician of international repute. This collection of his selected papers bears witness to the profound influence Levinson had on research in mathematical analysis with applications to problems in science and technology. Levinson's originality is reflected in his fundamental contributions to complex, harmonic and stochastic equations, and to analytic number theory, where he continued to make significant advances toward resolving the Riemann hypothesis up to the end of his life. The two volumes are divided by topic, with commentary by some of those who have felt the impact of Levinson's legacy.

目次

• Stability and asymptotic behaviour of solutions of ordinary differential equations
• nonlinear oscillations and dynamical systems
• inverse problems for Strum-Liouville and Schrodinger operators
• eigenfunction expansions and spectral theory for ordinary differential equations
• singular pertubations of ordinary and partial differential equations
• elliptic partial differential equations
• integral equations.

巻冊次

: set : Basel ISBN 9783764339784

内容説明

Norman Levinson (1912-1975) was a mathematician of international repute. This collection of his selected papers bears witness to the profound influence Levinson had on research in mathematical analysis with applications to problems in science and technology. Levinson's originality is reflected in his fundamental contributions to complex, harmonic and stochastic equations, and to analytic number theory, where he continued to make significant advances toward resolving the Riemann hypothesis up to the end of his life. The two volumes are divided by topic, with commentary by some of those who have felt the impact of Levinson's legacy.

目次

• Stability and asymptotic behaviour of solutions of ordinary differential equations
• nonlinear oscillations and dynamical systems
• inverse problems for Strum-Liouville and Schrodinger operators
• eigenfunction expansions and spectral theory for ordinary differential equations
• singular pertubations of ordinary and partial differential equations
• elliptic partial differential equations
• integral equations
• harmonic and complex an alysis
• stochastic analysis
• elementary number theory and the prime number theorem
• the Riemann-Zeta function
• zeros on the critical line
• omega results for the Riemann-Zeta function
• miscellaneous topics.

巻冊次

v. 2 : Basel ISBN 9783764339791

内容説明

Norman Levinson (1912-1975) was a mathematician of international repute. This collection of his selected papers bears witness to the profound influence Levinson had on research in mathematical analysis with applications to problems in science and technology. Levinson's originality is reflected in his fundamental contributions to complex, harmonic and stochastic equations, and to analytic number theory, where he continued to make significant advances toward resolving the Riemann hypothesis up to the end of his life. The two volumes are divided by topic, with commentary by some of those who have felt the impact of Levinson's legacy.

目次

• Harmonic and complex analysis
• stochastic analysis
• elementary number theory and the prime number theorem
• the Riemann-Zeta function
• zeros on the critical line
• omega results for the Riemann-Zeta function
• miscellaneous topics.

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詳細情報

• NII書誌ID(NCID): BA34137906
• ISBN:
  • 0817639780
  • 3764339780
  • 0817638628
  • 3764338628
  • 0817639799
  • 3764339799
• LCCN: 97038621
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Boston
• ページ数/冊数: 2 v.
• 大きさ: 27 cm
• 分類:
  • NDC8 : 410.4
  • LCC : QA3
  • DC21 : 515
• 件名:
  • LCSH : Mathematics
• 親書誌ID:
  • BA00145710