## Linear Partial Differential Operators in Gevrey Spaces

**Author**: Luigi Rodino

**Publisher:**World Scientific

**ISBN:**9789810208455

**Category:**Mathematics

**Page:**251

**View:**1800

**DOWNLOAD NOW »**

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

**DOWNLOAD NOW »**

## Advances in Pseudo-Differential Operators

**Author**: Ryuichi Ashino,Paolo Boggiatto,Man-Wah Wong

**Publisher:**Birkhäuser

**ISBN:**3034878400

**Category:**Mathematics

**Page:**236

**View:**9348

**DOWNLOAD NOW »**

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

**DOWNLOAD NOW »**

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

**DOWNLOAD NOW »**

## Linear Topological Spaces and Complex Analysis

**Author**: A. Aytuna

**Publisher:**N.A

**ISBN:**9789754290776

**Category:**Linear topological spaces

**Page:**125

**View:**3942

**DOWNLOAD NOW »**

## Proceedings workshop "Partial differential equations"

**Author**: Luigi Rodino

**Publisher:**N.A

**ISBN:**N.A

**Category:**Differential equations, Partial

**Page:**170

**View:**1815

**DOWNLOAD NOW »**

## Encyclopaedia of Mathematics

*Supplement*

**Author**: Michiel Hazewinkel

**Publisher:**Springer Science & Business Media

**ISBN:**9401512795

**Category:**Mathematics

**Page:**632

**View:**8552

**DOWNLOAD NOW »**

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

**DOWNLOAD NOW »**

## Indian Journal of Mathematics

**Author**: N.A

**Publisher:**N.A

**ISBN:**N.A

**Category:**Mathematics

**Page:**N.A

**View:**1035

**DOWNLOAD NOW »**

## 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

**DOWNLOAD NOW »**

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

**DOWNLOAD NOW »**

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

**DOWNLOAD NOW »**

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

**DOWNLOAD NOW »**

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

**DOWNLOAD NOW »**

## 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

**DOWNLOAD NOW »**

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

**DOWNLOAD NOW »**

## Microlocal Analysis and Spectral Theory

**Author**: Luigi Rodino

**Publisher:**Springer Science & Business Media

**ISBN:**9780792345442

**Category:**Mathematics

**Page:**444

**View:**3261

**DOWNLOAD NOW »**

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 SchrÃ¶dinger 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 (SchrÃ¶dinger 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

**DOWNLOAD NOW »**

## Bollettino Della Unione Matematica Italiana

**Author**: N.A

**Publisher:**N.A

**ISBN:**N.A

**Category:**Mathematics

**Page:**N.A

**View:**2113

**DOWNLOAD NOW »**