Microlocal analysis and complex Fourier analysis / editors, Takahiro Kawai, Keiko Fujita.

Format:

Book

Contributor:

Kawai, Takahiro.

Fujita, Keiko.

Kyōto Daigaku. Sūri Kaiseki Kenkyūjo.

Language:

English

Subjects (All):

Fourier analysis.

Microlocal analysis.

Functions of complex variables.

Physical Description:

1 online resource (339 p.)

Place of Publication:

River Edge, NJ : World Scientific, c2002.

Language Note:

English

Summary:

This book is a collection of original papers on microlocal analysis, Fourier analysis in the complex domain, generalized functions and related topics. Most of the papers originate from the talks given at the conference "Prospects of Generalized Functions" (in November, 2001 at RIMS, Kyoto). Reflecting the fact that the papers, except M Morimoto's one, are dedicated to Mitsuo Morimoto, the subjects considered in this book are interdisciplinary, just as Morimoto's works are. The historical backgrounds of the subjects are also discussed in depth in some contributions. Thus, this book should be va

Contents:

CONTENTS; Preface; Vanishing of Stokes Curves; 1 Introduction; 2 An equation with simple turning points; 3 A degenerate equation with simple turning points; 4 An equation with double turning points; 5 Conclusions; References; Parabolic Equations with Singularity on the Boundary; S1 Introduction; S2 Main Results; S3 Proof of Theorems; References; Residues: Analysis or Algebra?; References; Moment Conditions for Pompeiu Problem Extended to General Radial Surfaces; 1 Radial Moment Conditions for Pompeiu Problem on Cn; 2 Certain Moment Conditions on Disks for LP functions on Hn

3 Moments with Weighted Radial Measures on Disks and AnnuliReferences; Heat Equation via Generalized Functions; Introduction; 1 Notations and Preliminaries; 2 Uniqueness Theorems; 3 Example of Nonuniqueness; 4 Reflection Principles; References; Bergman Transformation for Analytic Functionals on Some Balls; Introduction; 1 Double series expansion; 2 Bilinear form of holomorphic functions on the Np-balls; 3 Bergman kernel for the Np-ball; 4 Bergman transformation; 5 Bergman kernel for the complex Euclidean ball; 6 Bergman kernel for the Lie ball; 7 Np-Fourier transformation; References

Explicit Construction of Fourier Hyperfunctions Supported at Infinity1 Introduction; 2 Holomorphic functions beyond the three-line theorem; 3 Construction of Fourier hyperfunctions supported at infinity; 4 Fourier ultradistributions supported at infinity; References; On Infra-Red Singularities Associated with QC Photons; 1 Introduction; 2 Characteristic features of the problem; 3 Study of some basic examples; References; On the Linear Hull of Exponentials in Cn and Applications to Convolution Equations; 1 Introduction; 2 Preliminaries; 3 An absolute basis of exponentials

4 An absolutely representing system of exponentials5 Convolution equations; 6 A particular solution; 7 A homogeneous equation; References; Hyperfunctions and Kernel Method; 1 Introduction; 2 Generalized functions as initial values of solutions of the heat equation; 3 Heat kernel method and hyperfunctions; References; Generalized Fourier Transformations: The Work of Bochner And Carleman Viewed in the Light of the Theories of Schwartz and Sato; 1 Introduction; 2 Bochner; 3 Streamlining Bochner's definition; 4 Carleman; 5 Schwartz; 6 Sato; 7 On Carleman's Fourier transformation

8 Lutzen's first question9 Lutzen's second question; 10 Conclusion; References; The Effect of New Stokes Curves in the Exact Steepest Descent Method; 1 Introduction - Brief review of exact steepest descent method and several problems of it; 2 The effect of a new Stokes curve; 3 The effect of a singular point of simple pole type; 4 The effect of a constant characteristic root; 5 Concluding remarks; References; Fourier's Hyperfunctions and Heaviside's Pseudodifferential Operators; 1 Fourier's S-function and operational calculus; 2 The heat equation and Fourier's boundary condition

3 Fourier's trigonometrical expansions and hyperfunctions

Notes:

"Some articles in this volume were read at the conference "Prospects of Generalized Functions", held from November 27 through November 30, 2001, at Research Institute for Mathematical Sciences, Kyoto University"--P. v.

Includes bibliographical references.

ISBN:

9786611929237

9781281929235

1281929239

9789812776594

9812776591