Tube domains and the Cauchy problem

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Tube Domains and the Cauchy Problem

Copyright
     ©1992 by the American Mathematical Society.
     ISBN 0-8218-4566-7
     ISBN-13: 978-0-8218-4566-0
     QA377.G5313 1992 515'.35-dc20
     LCCN 92-19406

Contents

Introduction

CHAPTER 1  The Cauchy Problem in Spaces of Distributions with Exponential Estimates

     §1. Spaces of functions (distributions) of exponential decrease (growth)

          1.1. Convex functions

          1.2. Holder scales corresponding to exponentially growing weight.

          1.3. Hilbert norms in Sµ and imbedding theorems

          1.4. Limit spaces for scales and the Fourier transform in them

          1.5. Spaces of exponentially growing functions and distributions.

     §2. Convolution operators and convolution equations

          2.1. Preliminary facts about multipliers

          2.2. Convolution operators and convolutors.

          2.3. The description of convolutors on Sµ

          2.4. Description of convolutors on Oµ

          2.5. Convolutors in spaces of functions and distributions of exponential growth

          2.6. Equations in convolutions in the spaces (\Phi_µ , '\Psi_µ

          2.7. Relation to the homogeneous Cauchy problem

          2.8. Exponentially correct differential operators

     §3. Convolution equations in a strip and the nonhomogeneous Cauchy problem for convolution equations

          3.1. Convolutors in a strip

          3.2. Convolution and differential equations in a strip

          3.3. Isotropic spaces

          3.4. Certain auxiliary results

          3.5. Function spaces associated to the nonhomogeneous Cauchy problem

          3.6. Exponential growth distributions with smoothness conditions

          3.7. Convolution and differential equations in (xD, l-'}' . The nonhomogeneous Cauchy problem

     §4. The Cauchy problem for exponentially correct differential operators with variable coefficients

          4.1. Exponentially correct differential operators of constant strength.

          4.2. Energy estimates for exponentially correct differential operators with variable coefficients.

     §5. Special classes of exponentially correct differential operators

          5.1. Hyperbolic operators

          5.2. 2b-parabolic operators

          5.3. N-parabolic operators

          5.4. Dominantly correct operators

          5.5. Pluriparabolic operators

          5.6. (2b + 1)-hyperbolic operators

CHAPTER 2  Strongly Homogeneous Differential Operators

     §1. The structure of affine-homogeneous domains

     §2. Compound power functions and Siegel integrals

     §3. Riemann-Liouville operators and differential operators associated to homogeneous cones

     §4. Analysis of fundamental solutions of differential operators related to linear-homogeneous cones

     §5. Pluriparabolic strongly homogeneous differential operators

References

Subject Index

Notation Index

Titles in This Series

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