Linear Partial Differential Operators in Gevrey Spaces


Author: Luigi Rodino
Publisher: World Scientific
ISBN: 9789810208455
Category: Mathematics
Page: 251
View: 1800
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The book is devoted to new and classical results of the theory of linear partial differential operators in Gevrey spaces. The ?microlocal approach? is adopted, by using pseudo-differential operators, wave front sets and Fourier integral operators.Basic results for Schwartz-distributions, cì and analytic classes are also included, concerning hypoellipticity, solvability and propagation of singularities.Also included is a self-contained exposition of the calculus of the pseudo-differential operators of infinite order.

General Theory of Partial Differential Equations and Microlocal Analysis


Author: Min-You Qi,L Rodino
Publisher: CRC Press
ISBN: 9780582292123
Category: Mathematics
Page: 240
View: 9860
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Advances in Pseudo-Differential Operators


Author: Ryuichi Ashino,Paolo Boggiatto,Man-Wah Wong
Publisher: Birkhäuser
ISBN: 3034878400
Category: Mathematics
Page: 236
View: 9348
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This volume consists of the plenary lectures and invited talks in the special session on pseudo-differential operators given at the Fourth Congress of the International Society for Analysis, Applications and Computation (ISAAC) held at York University in Toronto, August 11-16, 2003. The theme is to look at pseudo-differential operators in a very general sense and to report recent advances in a broad spectrum of topics, such as pde, quantization, filters and localization operators, modulation spaces, and numerical experiments in wavelet transforms and orthonormal wavelet bases.

Partial Differential Equations

Approximate Solutions in Scales of Functional Spaces
Author: Todor V. Gramchev,Petar R. Popivanov
Publisher: Wiley-VCH
ISBN: N.A
Category: Science
Page: 156
View: 3293
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The applications of methods from microlocal analysis for PDE have been a fast developing area during the last years. The authors, both are well known in the community, publish for the first time some of their research results in a summarized form. The essential point of the approach is the use of the various types of approximate (asymptotic) solutions in the study of differential equations in the smooth and the Gevrey spaces. In this volume, the authors deal with the following themes: Microlocal properties of pseudodifferential operators with multiple characteristics of involutive type in the framework of the Sobolev spaces; Abstract schemes for constructing approximate solutions to linear partial differential equations with characteristics of constant multiplicity m greater than or equal 2 in the framework of Gevrey spaces; Local solvability, hypoellipticity and singular solutions in Gevrey spaces; Global Gevrey solvability on the torus for linear partial differential equations; Applications of asymptotic methods for local (non)solvability for quasihomogeneous operators; Applications of Airy asymptotic solutions to degenerate oblique derivative problems for second order strictly hyperbolic equations; Approximate Gevrey normal forms of analytic involutions and analytic glancing hypersurfaces with applications for effective stability estimates for billiard ball maps.

Pseudo-Differential Operators and Related Topics


Author: Paolo Boggiatto,Luigi Rodino,Joachim Toft,M. W. Wong
Publisher: Springer Science & Business Media
ISBN: 3764375140
Category: Mathematics
Page: 244
View: 5066
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Linear Topological Spaces and Complex Analysis


Author: A. Aytuna
Publisher: N.A
ISBN: 9789754290776
Category: Linear topological spaces
Page: 125
View: 3942
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Proceedings workshop "Partial differential equations"


Author: Luigi Rodino
Publisher: N.A
ISBN: N.A
Category: Differential equations, Partial
Page: 170
View: 1815
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Encyclopaedia of Mathematics

Supplement
Author: Michiel Hazewinkel
Publisher: Springer Science & Business Media
ISBN: 9401512795
Category: Mathematics
Page: 632
View: 8552
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This is the second supplementary volume to Kluwer's highly acclaimed eleven-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing eleven volumes, and together these twelve volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.

Mathematical Reviews


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 4944
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Indian Journal of Mathematics


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 1035
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Differential Equations in Banach Spaces


Author: Giovanni Dore,Angelo Favini,Enrico Obrecht,Alberto Venni
Publisher: CRC Press
ISBN: 9780824790677
Category: Mathematics
Page: 288
View: 8639
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This reference - based on the Conference on Differential Equations, held in Bologna - provides information on current research in parabolic and hyperbolic differential equations. Presenting methods and results in semigroup theory and their applications to evolution equations, this book focuses on topics including: abstract parabolic and hyperbolic linear differential equations; nonlinear abstract parabolic equations; holomorphic semigroups; and Volterra operator integral equations.;With contributions from international experts, Differential Equations in Banach Spaces is intended for research mathematicians in functional analysis, partial differential equations, operator theory and control theory; and students in these disciplines.

Hyperbolic Differential Operators And Related Problems


Author: Vincenzo Ancona,Jean Vaillant
Publisher: CRC Press
ISBN: 9780203911143
Category: Mathematics
Page: 388
View: 7847
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Presenting research from more than 30 international authorities, this reference provides a complete arsenal of tools and theorems to analyze systems of hyperbolic partial differential equations. The authors investigate a wide variety of problems in areas such as thermodynamics, electromagnetics, fluid dynamics, differential geometry, and topology. Renewing thought in the field of mathematical physics, Hyperbolic Differential Operators defines the notion of pseudosymmetry for matrix symbols of order zero as well as the notion of time function. Surpassing previously published material on the topic, this text is key for researchers and mathematicians specializing in hyperbolic, Schrödinger, Einstein, and partial differential equations; complex analysis; and mathematical physics.

Degenerate Differential Equations in Banach Spaces


Author: Angelo Favini,Atsushi Yagi
Publisher: CRC Press
ISBN: 9780824716776
Category: Mathematics
Page: 336
View: 2066
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This work presents a detailed study of linear abstract degenerate differential equations, using both the semigroups generated by multivalued (linear) operators and extensions of the operational method from Da Prato and Grisvard. The authors describe the recent and original results on PDEs and algebraic-differential equations, and establishes the analyzability of the semigroup generated by some degenerate parabolic operators in spaces of continuous functions.

Divergent Series, Summability and Resurgence II

Simple and Multiple Summability
Author: Michèle Loday-Richaud
Publisher: Springer
ISBN: 3319290754
Category: Mathematics
Page: 272
View: 2099
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Addressing the question how to “sum” a power series in one variable when it diverges, that is, how to attach to it analytic functions, the volume gives answers by presenting and comparing the various theories of k-summability and multisummability. These theories apply in particular to all solutions of ordinary differential equations. The volume includes applications, examples and revisits, from a cohomological point of view, the group of tangent-to-identity germs of diffeomorphisms of C studied in volume 1. With a view to applying the theories to solutions of differential equations, a detailed survey of linear ordinary differential equations is provided, which includes Gevrey asymptotic expansions, Newton polygons, index theorems and Sibuya’s proof of the meromorphic classification theorem that characterizes the Stokes phenomenon for linear differential equations. This volume is the second in a series of three, entitled Divergent Series, Summability and Resurgence. It is aimed at graduate students and researchers in mathematics and theoretical physics who are interested in divergent series, Although closely related to the other two volumes, it can be read independently.

Singularities and differential equations


Author: Stanisław Janeczko,Wojciech M. Zajączkowski,Bogdan Ziemian
Publisher: N.A
ISBN: N.A
Category: Differential equations, Partial
Page: 501
View: 2042
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Advances in Phase Space Analysis of Partial Differential Equations

In Honor of Ferruccio Colombini's 60th Birthday
Author: Antonio Bove,Daniele Del Santo,M.K. Venkatesha Murthy
Publisher: Springer Science & Business Media
ISBN: 0817648615
Category: Mathematics
Page: 292
View: 9182
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This collection of original articles and surveys addresses the recent advances in linear and nonlinear aspects of the theory of partial differential equations. The key topics include operators as "sums of squares" of real and complex vector fields, nonlinear evolution equations, local solvability, and hyperbolic questions.

Reviews in partial differential equations, 1980-86, as printed in Mathematical reviews


Author: American Mathematical Society
Publisher: N.A
ISBN: N.A
Category: Differential equations, Partial
Page: 3998
View: 8991
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Microlocal Analysis and Spectral Theory


Author: Luigi Rodino
Publisher: Springer Science & Business Media
ISBN: 9780792345442
Category: Mathematics
Page: 444
View: 3261
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There has been considerable recent progress in the field of microlocal analysis. In a broad sense the subject is the modern version of the classical Fourier technique for solving partial differential equations, with the localization process taking account of dual variables. The tools of pseudo-differential operators, wave-front sets and Fourier integral operators have now conferred a mature form on the theory of linear partial differential operators in the frame of Schwartz distributions or other generalized functions. At the same time, microlocal analysis has assumed an important role as an independent part of analysis, with other applications throughout mathematics and physics, one major theme being spectral theory for the Schrödinger equation in quantum mechanics. The papers collected here emphasize the topics of microlocal methods in the study of linear PDEs (analytic-Gevrey regularity of the solutions, elliptic boundary value problems, higher microlocalization), and applications to spectral theory (Schrödinger equation, asymptotic behavior of the eigenvalues, semi-classical analysis in large dimensions and statistical mechanics). Audience: Accessible to a wide audience, including graduate students in analysis and non-specialists from mathematics and physics.

Partial Differential Equations and Mathematical Physics

In Memory of Jean Leray
Author: Kunihiko Kajitani,Jean Vaillant
Publisher: Springer Science & Business Media
ISBN: 1461200113
Category: Mathematics
Page: 243
View: 4711
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Bollettino Della Unione Matematica Italiana


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 2113
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