Based on a seminar sponsored by the Institute for Advanced Study in 1977-1978, this set of papers introduces micro-local analysis concisely and clearly to mathematicians with an analytical background. The papers treat the theory of microfunctions and applications such as boundary values of elliptic partial differential equations, propagation of singularities in the vicinity of degenerate characteristics, holonomic systems, Feynman integrals from the hyperfunction point of view, and harmonic analysis on Lie groups.

Seminar on Micro-Local Analysis (Annals of Mathematics Studies)

Science & Math

Guillemin, Victor

Kashiwara, Masaki

Kawai, Takahiro

Mathematics

Princeton University Press

Based on a seminar sponsored by the Institute for Advanced Study in 1977-1978, this set of papers introduces micro-local analysis concisely and clearly to mathematicians with an analytical background. The papers treat the theory of microfunctions and applications such as boundary values of elliptic partial differential equations, propagation of singularities in the vicinity of degenerate characteristics, holonomic systems, Feynman integrals from the hyperfunction point of view, and harmonic analysis on Lie groups.

The use of algebraic methods for studying analysts is an important theme in modern mathematics. The most significant development in this field is microlocal analysis, that is, the local study of differential equations on cotangent bundles. This treatise provides a thorough description of microlocal analysis starting from its foundations. The book begins with the definition of a hyperfunction. It then carefully develops the microfunction theory and its applications to differential equations and theoretical physics. It also provides a description of microdifferential equations, the microlocalization of linear differential equations. Finally, the authors present the structure theorems for systems of microdifferential equations, where the quantized contact transformations are used as a fundamental device.
The microfunction theory, together with the quantized contact transformation theory, constitutes a valuable new viewpoint in linear partial differential equations.
Originally published in 1986.
The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Foundations of Algebraic Analysis (Princeton Mathematical Series, 37)

Kimura, Tatsuo

The use of algebraic methods for studying analysts is an important theme in modern mathematics. The most significant development in this field is microlocal analysis, that is, the local study of differential equations on cotangent bundles. This treatise provides a thorough description of microlocal analysis starting from its foundations. The book begins with the definition of a hyperfunction. It then carefully develops the microfunction theory and its applications to differential equations and theoretical physics. It also provides a description of microdifferential equations, the microlocalization of linear differential equations. Finally, the authors present the structure theorems for systems of microdifferential equations, where the quantized contact transformations are used as a fundamental device.The microfunction theory, together with the quantized contact transformation theory, constitutes a valuable new viewpoint in linear partial differential equations.Originally published in 1986.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

The topic of this book is the study of singular perturbations of ordinary differential equations, i.e., perturbations that represent solutions as asymptotic series rather than as analytic functions in a perturbation parameter. The main method used is the so-called WKB (Wentzel-Kramers-Brillouin) method, originally invented for the study of quantum-mechanical systems. The authors describe in detail the WKB method and its applications to the study of monodromy problems for Fuchsian differential equations and to the analysis of Painleve functions. The volume is suitable for graduate students and researchers interested in differential equations and special functions.

Algebraic Analysis of Singular Perturbation Theory (IWANAMI SERIES IN MODERN MATHEMATICS: TRANSLATIONS OF MATHEMATICAL MONOGRAPHS, 227)

Takei, Yoshitsugu

Amer Mathematical Society

This is a collection of papers on current topics and future problems in the theory of differential equations which were reported at the Taniguchi symposium (Katata) and RIMS symposium (Kyoto). It includes topics such as: Painleve transcendents; Borel resummation; linear differential equations of infinite order; Jacobi-type differential equations for automorphic forms; and Gevrey index.

Structure of Solutions of Differential Equations

World Scientific Publishing Company

See the best price to sell, buy, or rent books by Kawai, Takahiro. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Kawai, Takahiro

See the best price to sell, buy, or rent books by Kawai, Takahiro. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Seminar on Micro-Local Analysis (Annals of Mathematics Studies)

Seminar on Micro-Local Analysis (Annals of Mathematics Studies)

Foundations of Algebraic Analysis (Princeton Mathematical Series, 37)

Foundations of Algebraic Analysis (Princeton Mathematical Series, 37)

Foundations of Algebraic Analysis (Princeton Mathematical Series, 37)

Algebraic Analysis of Singular Perturbation Theory (IWANAMI SERIES IN MODERN MATHEMATICS: TRANSLATIONS OF MATHEMATICAL MONOGRAPHS, 227)

Structure of Solutions of Differential Equations