Fundamentals of Algebraic Microlocal Analysis

Fundamentals of Algebraic Microlocal Analysis

"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.

Author: Goro Kato

Publisher: CRC Press

ISBN: 9781000148398

Category: Mathematics

Page: 230

View: 236

"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."
Categories: Mathematics

Advances in Microlocal and Time Frequency Analysis

Advances in Microlocal and Time Frequency Analysis

Kato,G. and Struppa,D.C.: Fundamentals of algebraic microlocal analysis. Monographs and Textbooks in Pure and Applied Mathematics, vo. 217, Marcel Dekker, Inc., New York, 1999, xii+296 pp. Kiselman,C.O.: Generalized Fourier ...

Author: Paolo Boggiatto

Publisher: Springer Nature

ISBN: 9783030361389

Category: Mathematics

Page: 525

View: 138

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.
Categories: Mathematics

Fundamentals of Advanced Mathematics 2

Fundamentals of Advanced Mathematics 2

... Fundamentals of Algebraic Microlocal Analysis, Marcel Dekker, 1999. [KAU83] KAUP L., KAUP B., Holomorphic Functions of Several Variables, Walter de Gruyter, 1983. [KEL 55] KELLEY J., General Topology, van Nostrand, 1955.

Author: Henri Bourles

Publisher: Elsevier

ISBN: 9780081023853

Category: Mathematics

Page: 360

View: 786

The three volumes of this series of books, of which this is the second, put forward the mathematical elements that make up the foundations of a number of contemporary scientific methods: modern theory on systems, physics and engineering. Whereas the first volume focused on the formal conditions for systems of linear equations (in particular of linear differential equations) to have solutions, this book presents the approaches to finding solutions to polynomial equations and to systems of linear differential equations with varying coefficients. Fundamentals of Advanced Mathematics, Volume 2: Field Extensions, Topology and Topological Vector Spaces, Functional Spaces, and Sheaves begins with the classical Galois theory and the theory of transcendental field extensions. Next, the differential side of these theories is treated, including the differential Galois theory (Picard-Vessiot theory of systems of linear differential equations with time-varying coefficients) and differentially transcendental field extensions. The treatment of analysis includes topology (using both filters and nets), topological vector spaces (using the notion of disked space, which simplifies the theory of duality), and the radon measure (assuming that the usual theory of measure and integration is known). In addition, the theory of sheaves is developed with application to the theory of distributions and the theory of hyperfunctions (assuming that the usual theory of functions of the complex variable is known). This volume is the prerequisite to the study of linear systems with time-varying coefficients from the point-of-view of algebraic analysis and the algebraic theory of nonlinear systems. Present Galois Theory, transcendental field extensions, and Picard Includes sections on Vessiot theory, differentially transcendental field extensions, topology, topological vector spaces, Radon measure, differential calculus in Banach spaces, sheaves, distributions, hyperfunctions, algebraic analysis, and local analysis of systems of linear differential equations
Categories: Mathematics

Analysis of Dirac Systems and Computational Algebra

Analysis of Dirac Systems and Computational Algebra

[90 L, Hörmander, An Introduction to Complex Analysis in Several Variables, Van Nostrand, Princeton, 1966. [91]. L. Hörmander, The analysis of Linear Partial ... Algebraic Microlocal Analysis, Marcel Dekker Inc., New York, 1999.

Author: Fabrizio Colombo

Publisher: Springer Science & Business Media

ISBN: 9780817681661

Category: Mathematics

Page: 332

View: 484

* The main treatment is devoted to the analysis of systems of linear partial differential equations (PDEs) with constant coefficients, focusing attention on null solutions of Dirac systems * All the necessary classical material is initially presented * Geared toward graduate students and researchers in (hyper)complex analysis, Clifford analysis, systems of PDEs with constant coefficients, and mathematical physics
Categories: Mathematics

Algebraic Geometry for Associative Algebras

Algebraic Geometry for Associative Algebras

Young, Vector and Tensor Analysis: Second Edition (1993) Bick, Elementary Boundary Value Problems (1993) C. A. Pavel, ... Fundamentals and Recent Advances (1999) G. Kato and D. Struppa, Fundamentals of Algebraic Microlocal Analysis ...

Author: Freddy Van Oystaeyen

Publisher: CRC Press

ISBN: 9781482270525

Category: Mathematics

Page: 302

View: 756

This work focuses on the association of methods from topology, category and sheaf theory, algebraic geometry, noncommutative and homological algebras, quantum groups and spaces, rings of differential operation, Cech and sheaf cohomology theories, and dimension theories to create a blend of noncommutative algebraic geometry. It offers a scheme theor
Categories: Mathematics

Abstract Algebra

Abstract Algebra

E. C. Young , Vector and Tensor Analysis : Second Edition ( 1993 ) 173. ... M. Pavel , Fundamentals of Pattern Recognition : Second Edition ( 1993 ) 175. ... Fundamentals of Algebraic Microlocal Analysis ( 1999 ) 218.

Author: Claudia Menini

Publisher: CRC Press

ISBN: 9781482258172

Category: Mathematics

Page: 776

View: 338

In one exceptional volume, Abstract Algebra covers subject matter typically taught over the course of two or three years and offers a self-contained presentation, detailed definitions, and excellent chapter-matched exercises to smooth the trajectory of learning algebra from zero to one. Field-tested through advance use in the ERASMUS educational project in Europe, this ambitious, comprehensive book includes an original treatment of representation of finite groups that avoids the use of semisimple ring theory and explains sets, maps, posets, lattices, and other essentials of the algebraic language; Peano's axioms and cardinality; groupoids, semigroups, monoids, groups; and normal subgroups.
Categories: Mathematics

Hopf Algebra

Hopf Algebra

M. Pavel , Fundamentals of Pattern Recognition : Second Edition ( 1993 ) 175. ... G. Kato and D. Struppa , Fundamentals of Algebraic Microlocal Analysis ( 1999 ) 218. G. X.-Z. Yuan , KKM Theory and Applications in Nonlinear Analysis ...

Author: Sorin Dascalescu

Publisher: CRC Press

ISBN: 0824704819

Category: Mathematics

Page: 428

View: 335

This study covers comodules, rational modules and bicomodules; cosemisimple, semiperfect and co-Frobenius algebras; bialgebras and Hopf algebras; actions and coactions of Hopf algebras on algebras; finite dimensional Hopf algebras, with the Nicholas-Zoeller and Taft-Wilson theorems and character theory; and more.
Categories: Mathematics

A Primer of Algebraic Geometry

A Primer of Algebraic Geometry

E. C. Young , Vector and Tensor Analysis : Second Edition ( 1993 ) 173. T. A. Bick , Elementary Boundary ... M. Pavel , Fundamentals of Pattern Recognition : Second Edition ( 1993 ) 175. ... Algebraic Microlocal Analysis ( 1999 ) 218.

Author: Huishi Li

Publisher: CRC Press

ISBN: 082470374X

Category: Mathematics

Page: 398

View: 391

"Presents the structure of algebras appearing in representation theory of groups and algebras with general ring theoretic methods related to representation theory. Covers affine algebraic sets and the nullstellensatz, polynomial and rational functions, projective algebraic sets. Groebner basis, dimension of algebraic sets, local theory, curves and elliptic curves, and more."
Categories: Mathematics

Algebraic Generalizations of Discrete Groups

Algebraic Generalizations of Discrete Groups

M. Pavel , Fundamentals of Pattern Recognition : Second Edition ( 1993 ) 175. ... G. Kato and D. Struppa , Fundamentals of Algebraic Microlocal Analysis ( 1999 ) 218. G. X.-Z. Yuan , KKM Theory and Applications in ...

Author: Benjamin Fine

Publisher: CRC Press

ISBN: 0824703197

Category: Mathematics

Page: 338

View: 575

A survey of one-relator products of cyclics or groups with a single defining relation, extending the algebraic study of Fuchsian groups to the more general context of one-relator products and related group theoretical considerations. It provides a self-contained account of certain natural generalizations of discrete groups.
Categories: Mathematics

Applied Functional Analysis

Applied Functional Analysis

V.I.Amautov et al., Introduction to the Theory of Topological Rings and Modules (1996) 198. ... R.Lasser, Introduction to Fourier Series (1996) 200. ... G.Kato and D.Struppa, Fundamentals of Algebraic Microlocal Analysis (1999) 218.

Author: Abul Hasan Siddiqi

Publisher: CRC Press

ISBN: 9780824756628

Category: Mathematics

Page: 536

View: 562

The methods of functional analysis have helped solve diverse real-world problems in optimization, modeling, analysis, numerical approximation, and computer simulation. Applied Functional Analysis presents functional analysis results surfacing repeatedly in scientific and technological applications and presides over the most current analytical and numerical methods in infinite-dimensional spaces. This reference highlights critical studies in projection theorem, Riesz representation theorem, and properties of operators in Hilbert space and covers special classes of optimization problems. Supported by 2200 display equations, this guide incorporates hundreds of up-to-date citations.
Categories: Mathematics