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Band 10

Tauberian Theorems for Generalized Functions

Aus der Reihe Mathematics and its Applications

Fr. 137.00

inkl. gesetzl. MwSt., Versandkostenfrei

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

02.10.2011

Verlag

Springer Netherland

Seitenzahl

293

Maße (L/B/H)

23.5/15.5/1.7 cm

Auflage

Reprint of the original 1st ed. 1988

Sprache

Englisch

ISBN

978-94-010-7774-3

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

02.10.2011

Verlag

Springer Netherland

Seitenzahl

293

Maße (L/B/H)

23.5/15.5/1.7 cm

Auflage

Reprint of the original 1st ed. 1988

Sprache

Englisch

ISBN

978-94-010-7774-3

Herstelleradresse

Springer-Verlag KG
Sachsenplatz 4-6
1201 Wien
AT

Email: GPSR Kontakt

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  • Produktbild: Tauberian Theorems for Generalized Functions
  • Produktbild: Tauberian Theorems for Generalized Functions
  • Notation and Definitions.- 1: Some Facts on the Theory of Distributions.- 1. Distributions and their properties.- 1. Spaces of test functions.- 2. The space of distributions D?(O).- 3. The space of distributions S?(F).- 4. Linear operations on distributions.- 5. Change of variables.- 6. L -invariant distributions.- 7. Direct product of distributions.- 8. Convolution of distributions.- 9. Convolution algebras of distributions.- 2. Integral transformations of distributions.- 1. The Fourier transform of tempered distributions.- 2. Fourier series of periodic distributions.- 3. The B -transform of distributions.- 4. Fractional derivatives (primitives).- 5. The Laplace transform of tempered distributions.- 6. The Cauchy kernel of the tube domain TC.- 7. Regular cones.- 8. Fractional derivatives (primitives) with respect to a cone.- 9. The Radon transform of distributions with compact support in an odd-dimensional space.- 3. Quasi-asymptotics of distributions.- 1. General definitions and basic properties.- 2. Automodel (regularly varying) functions.- 3. Quasi-asymptotics over one-parameter groups of transformations.- 4. The one-dimensional case. Quasi-asymptotics at infinity and at zero.- 5. The one-dimensional case. Asymptotics by translations.- 6. Quasi-asymptotics by selected variable.- 2: Many-Dimensional Tauberian Theorems.- 4. The General Tauberian theorem and its consequences.- 1. The Tauberian theorem for a family of linear transformations.- 2. The general Tauberian theorem for the dilatation group.- 3. Tauberian theorems for nonnegative measures.- 4. Tauberian theorems for holomorphic functions of bounded argument.- 5. Admissible and strictly admissible functions.- 1. Families of linear transformations under which a cone is invariant.- 2. Strictly admissible functions for a family of linear transformations.- 3. Admissible functions of a cone.- 4. Some examples of admissible functions of a cone.- 6. Comparison Tauberian theorems.- 1. Preliminary theorems.- 2. The comparison Tauberian theorems for measures and for holomorphic functions with nonnegative imaginary part.- Comments on Chapter 2.- 3: One-Dimensional Tauberian Theorems.- 7. The general Tauberian theorem and its consequences.- 1. The general Tauberian theorem and its particular cases.- 2. Quasi-asymptotics of a distribution f from S+? and a function arg f?.- 3. Tauberian theorem for distributions from the class .- 4. The decomposition theorem.- 8. Quasi-asymptotic properties of distributions at the origin.- 1. The general case.- 2. Quasi-asymptotics of distributions from H and asymptotic properties of the reproducting functions of measures.- 9. Asymptotic properties of the Fourier transform of distributions from M+.- 1. Asymptotic properties of the Fourier transform of finite measures.- 2. Asymptotic properties of the Fourier transform of distributions from M+.- 3. The Abel and Cezaro series summation with respect to an automodel weight.- 10. Quasi-asymptotic expansions.- 1. Open and closed quasi-asymptotic expansions.- 2. Quasi-asymptotic expansions and convolutions.- 4: Asymptotic Properties of Solutions of Convolutions Equations.- 11. Quasi-asymptotics of the fundamental solutions of convolution equations.- 1. Quasi-asymptotics and convolution.- 2. Quasi-asymptotics of the fundamental solutions of hyperbolic operators with constant coefficients.- 3. Quasi-asymptotics of the solutions of the Cauchy problem for the heat equation.- 12. Quasi-asymptotics of passive operators.- 1. The translationally-invariant passive operators.- 2. The fundamental solution and the Cauchy problem.- 3. Quasi-asymptotics of passive operators and their fundamental solutions.- 4. Differential operators of the passive type.- 5. Examples.- Comments on Chapter 4.- 5: Tauberian Theorems for Causal Functions.- 13. The Jost-Lehmann-Dyson representation.- 1. The Jost-Lehmann-Dyson representation in the symmetric case.- 2. Inversion of the Jost-Lehmann-Dyson representation in the symmetric case.- 3. The Jost-Lehmann-Dyson representation in the general case.- 14. Automodel asymptotics for the causal functions and singularities of their Fourier transforms on the light cone.- 1. Some preliminary results and definitions.- 2. The main theorems.- 3. On forbidden asymptotics in the Björken domain.- 4. Asymptotic properties of the two-point Wightman function.- Comments on Chapter 5.