Microlocal Analysis And Complex Fourier Analysis

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 valuable not only to the specialists in the fields, but also to those who are interested in the history of modern mathematics such as distributions and hyperfunctions. Contents:Vanishing of Stokes Curves (T Aoki et al.)Parabolic Equations with Singularity on the Boundary (C P Arceo et al.)Residues: Analysis or Algebra? (C A Berenstein)Heat Equation via Generalized Functions (S-Y Chung)Bergman Transformation for Analytic Functionals on Some Balls (K Fujita)On Infra-Red Singularities Associated with QC Photons (T Kawai & H P Stapp)Hyperfunctions and Kernel Method (D Kim)The Effect of New Stokes Curves in the Exact Steepest Descent Method (T Koike & Y Takei)Boehmians on the Sphere and Zonal Spherical Functions (M Morimoto)On a Generalization of the Laurent Expansion (Y Saburi)Domains of Convergence of Laplace Series (J Siciak)The Reproducing Kernels of the Space of Harmonic Polynomials in the Case of Real Rank 1 (R Wada & Y Agaoka)and other papers Readership: Graduate students in analysis or differential geometry and specialists in generalized functions, differential equations, analytic functions and complex WKB analysis. Keywords:

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 OC Prospects of Generalized FunctionsOCO (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 valuable not only to the specialists in the fields, but also to those who are interested in the history of modern mathematics such as distributions and hyperfunctions."

The NATO Advanced Study Institute "Microlocal Analysis and Spectral The ory" was held in Tuscany (Italy) at Castelvecchio Pascoli, in the district of Lucca, hosted by the international vacation center "11 Ciocco" , from September 23 to October 3, 1996. The Institute recorded the considerable progress realized recently in the field of Microlocal Analysis. In a broad sense, Microlocal Analysis is the modern version of the classical Fourier technique in solving partial differential equa tions, where now the localization proceeding takes place with respect to the dual variables too. Precisely, through the tools of pseudo-differential operators, wave-front sets and Fourier integral operators, the general theory of the lin ear partial differential equations is now reaching a mature form, in the frame of Schwartz distributions or other generalized functions. At the same time, Microlocal Analysis has grown up into a definite and independent part of Math ematical Analysis, with other applications all around Mathematics and Physics, one major theme being Spectral Theory for Schrodinger equation in Quantum Mechanics.

"Provides a thorough introduction to the algebraic theory of systems of differential equations, as developed by the Japanese school of M. Sato and his colleagues. Features a complete review of hyperfunction-microfunction theory and the theory of D-modules. Strikes the perfect balance between analytic and algebraic aspects."

This book presents contributions from two workshops in algebraic and analytic microlocal analysis that took place in 2012 and 2013 at Northwestern University. Featured papers expand on mini-courses and talks ranging from foundational material to advanced research-level papers, and new applications in symplectic geometry, mathematical physics, partial differential equations, and complex analysis are discussed in detail. Topics include Procesi bundles and symplectic reflection algebras, microlocal condition for non-displaceability, polarized complex manifolds, nodal sets of Laplace eigenfunctions, geodesics in the space of Kӓhler metrics, and partial Bergman kernels. This volume is a valuable resource for graduate students and researchers in mathematics interested in understanding microlocal analysis and learning about recent research in the area.

The present volume gathers contributions to the conference Microlocal and Time-Frequency Analysis 2018 (MLTFA18), which was held at Torino University from the 2nd to the 6th of July 2018. The event was organized in honor of Professor Luigi Rodino on the occasion of his 70th birthday. The conference’s focus and the contents of the papers reflect Luigi’s various research interests in the course of his long and extremely prolific career at Torino University.

CONTENTS: J.M. Bony: Analyse microlocale des equations aux derivees partielles non lineaires.- G.G. Grubb: Parabolic pseudo-differential boundary problems and applications.- L. H|rmander: Quadratic hyperbolic operators.- H. Komatsu: Microlocal analysis in Gevrey classes and in complex domains.- J. Sj|strand: Microlocal analysis for the periodic magnetic Schr|dinger equation and related questions.