Selected Works of Norman Levinson

Inbunden, Engelska, 1997

AvNorman Levinson,John Nohel,David Sattinger,G.-C. Rota,G. -C. Rota

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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.

Produktinformation

Utgivningsdatum1997-12-18
Mått178 x 254 x 73 mm
Vikt2 547 g
FormatInbunden
SpråkEngelska
SerieContemporary Mathematicians
Antal sidor536
Upplaga1997
FörlagBirkhauser Boston Inc
ISBN9780817639785

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— 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), ABoundary 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).