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Friday, July 10, 2020 | History

2 edition of Pseudo-differential and Mellin operators in spaces with conormal singularity (boundary symbols) found in the catalog.

Pseudo-differential and Mellin operators in spaces with conormal singularity (boundary symbols)

Stephan Rempel

Pseudo-differential and Mellin operators in spaces with conormal singularity (boundary symbols)

by Stephan Rempel

  • 149 Want to read
  • 39 Currently reading

Published by Akademie der Wissenschaften der DDR, Institut für Mathematik in Berlin .
Written in English

    Subjects:
  • Pseudodifferential operators.,
  • Mellin operators.,
  • Boundary value problems.,
  • Function spaces.

  • Edition Notes

    StatementStephan Rempel and Bert-Wolfgang Schulze.
    SeriesReport / Akademie der Wissenschaften der DDR, Institut für Mathematik,, R-MATH 01/84, Report (Akademie der Wissenschaften der DDR. Institut für Mathematik) ;, R-Math-84/01.
    ContributionsSchulze, Bert-Wolfgang.
    Classifications
    LC ClassificationsQA329.7 .R46 1984
    The Physical Object
    Paginationvii, 96 p. ;
    Number of Pages96
    ID Numbers
    Open LibraryOL2971824M
    LC Control Number84218948

    Boundary Value Problems and Singular Pseudo-differential Operators covers the analysis of pseudo-differential operators on manifolds with conical points and edges. The standard singular integral operators on the half-axis as well as boundary value problems on smooth manifolds are treated as particular cone and wedge theories. I think the third volume of Hormander's The Analysis of Linear Partial Differrential Operators is a good reference. chapter 18 is an introduction to PsDOs, especially, in section , it's devoted to conormal distributions, which I think is very useful for people with PsDO background.

    Pseudo-Differential Operators, Singularities, Applications It seems that you're in USA. We have a dedicated site for Pseudo-Differential Operators, Singularities, Applications. Authors: Egorov, Youri, Pseudo-differential operators on manifolds with conical singularities. Pages Pseudo-Differential Operators: Theory and Applications is a series of moderately priced graduate-level textbooks and monographs appealing to students and experts alike. Pseudo-differential operators are understood in a very broad sense and include such topics as harmonic analysis, PDE, geometry, mathematical physics, microlocal analysis, time.

    We construct Mellin quantisations or operator conventions, applied to corner-degenerate pseudo-differential symbols, referring to geometric corners of singularity order k∈ℕ, and we obtain. Pseudo-differential and Mellin operators in spaces with conormal singularity. MR ; Thomas Runst and Winfried Sickel, Sobolev spaces of fractional order, Nemytskij operators, and nonlinear partial differential equations, De Gruyter Series in Nonlinear Analysis and Applications, vol. 3, Walter de Gruyter & Co., Berlin, MR


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Pseudo-differential and Mellin operators in spaces with conormal singularity (boundary symbols) by Stephan Rempel Download PDF EPUB FB2

S. Rempel, B.-W. Schulze: Asymptotics for elliptic mixed boundary problems (pseudo-differential and Mellin operators in spaces with conormal singularity).

Math. Research Series, Akademie Verlag Berlin (to appear ) Google ScholarCited by: 9. The present book is devoted to elliptic partial differential equations in the framework of pseudo-differential operators. The first chapter contains the Mellin pseudo-differential calculus on R+ and the functional analysis of weighted Sobolev spaces with discrete and continuous asymptotics.

Chapter 2 is devoted to the analogous theory on manifolds with conical singularities, Chapter 3 to Book Edition: 1. It is well-known that the parametrices of elliptic partial differential equations on C ∞ manifolds (say closed compact or compact with C ∞ boundary) can be expressed by pseudo-differential operators.

This implies the elliptic regularity in terms of (for instance) the standard Sobolev by:   R empel, S., S chulze, B.-W.: Asymptotics for elliptic mixed boundary problems (pseudo-differential and Mellin operators in spaces with conormal singularity). Math. Research Ser Akademie-Verlag, Berlin Cited by: —, Asymptotics for elliptic mixed boundary problems (Pseudo-differential and Mellin operators in spaces with conormal singularity).

Mathematics Research Series, Akademie-Verlag Berlin (to appear ). Google ScholarCited by: From the Publisher. This book covers the analysis of pseudo-differential operators on manifolds with conical points and edges.

The standard singular integral operators on the half-axis as well as boundary value problems on smooth manifolds are treated as particular cone and wedge theories. The standard calculus of pseudo-differential and Fourier integral operators may today be considered as classical.

The development has been continuous since the early days of the first essential applications to ellip­ ticity, index theory, parametrices and propagation of singularities for non-elliptic operators, boundary-value problems, and Reviews: 1. The Mellin Expansion of Operators. Operators on Manifolds with Conical Singularities.

Spaces with Conormal Asymptotics for the Cone. The Mellin Expansions for the Cone. The Parameter-Dependent Cone Calculus. Operators on Manifolds with Edges.

Preliminary Constructions. Pseudo-Differential Operators with Operator-Valued Symbols. Pseudo. Pseudo-Differential Operators, Singularities, Applications I͡Uriĭ Vladimirovich Egorov Springer Science & Business Media, - Fourier integral operators - pages. Singularities in Differential Equations Singularities often of important physical significance.

Further, useful in Painleve-testfor integrability For linear systems, singularities where coefficients or inhomogeneous term singular Not true for nonlinear diff.

equations. Eg.: Movable singularities depend on initial conditions. Difficult to. Read the latest chapters of Studies in Mathematics and Its Applications atElsevier’s leading platform of peer-reviewed scholarly literature. Properties. Linear differential operators of order m with smooth bounded coefficients are pseudo-differential operators of order composition PQ of two pseudo-differential operators P, Q is again a pseudo-differential operator and the symbol of PQ can be calculated by using the symbols of P and adjoint and transpose of a pseudo-differential operator is a pseudo-differential operator.

Pseudo-differential operators on manifolds with singularities. -- The analysis of differential equations in domains and on manifolds with singularities belongs to the main streams of recent developments in applied and pure mathematics.

The Mellin Transform. Spaces with Conormal Asymptotics. The Mellin Expansion of Operators. Operators on. We study Volterra property and parabolicity of a class of anisotropic pseudo-differential operators on a manifold with edge. This exposition belongs to a more comprehensive approach.

In the present consideration we focus on asymptotic aspects of parametrices or inverses in the subalgebra of anisotropic operators of Mellin plus Green type.

Pseudo-differential and Mellin operators in spaces with conormal singularity. MR ; B.-W. Schulze, Pseudo-differential operators on manifolds with singularities, Studies in Mathematics and its Applications, vol.

24, North-Holland Publishing Co., Amsterdam, MR ; The first article prepares the ground by presenting a calculus for pseudo differential operators with an anisotropic analytic parameter. In the subsequent paper, an algebra of Mellin operators on the infinite space-time cylinder is constructed.

It is shown how timelike infinity can be treated as a conical singularity. The ellipticity of any such operator A refers to a pair of principal symbols (σ 0, σ 1) where σ 0 is the standard (degenerate) homogeneous principal symbol, and σ 1 is the so-called conormal.

In particular, it considers parameter-dependent edge operators and edge operators of Mellin type. The investigation of such operator families is necessary to construct operator algebras on manifolds with higher singularities.

A self-contained exposition in Mellin techniques and pseudodifferential operators with operator-valued symbols is given. Get this from a library.

Pseudo-Differential Operators, Singularities, Applications. [I︠U︡ V Egorov; Bert-Wolfgang Schulze] -- This book grew out of lecture notes based on the DMV seminar "Pseudo- Differential Operators, Singularities, Applications" held by the authors in Reisenburg-Günzburg, July The modern.

Calculus of Pseudo-Differential Operators and a Local Index of Dirac Operators and Mellin operators in spaces with conormal singularity Theorem by the symbolic calculus of pseudo. Introduction to pseudo-di erential operators Michael Ruzhansky Janu Abstract The present notes give introduction to the theory of pseudo-di erential oper-ators on Euclidean spaces.

The rst part is devoted to the necessary analysis of functions, such as basics of the Fourier analysis and the theory of distributions and Sobolev spaces.The International Workshop on Pseudo-Di?erential Operators: Complex Analysis and Partial Di?erential Equations was held at York University on August 4 8, The?rst phase of the workshop on August 4 5 consisted of a mini-course on pseudo-di?erential operators and boundary value problems given by Professor Bert-Wolfgang Schulze of Universita Format: Hardcover.Pseudo-differential operators were initiated by Kohn, Nirenberg and Hörmander in the sixties of the last century.

Beside applications in the general theory of partial differential equations, they have their roots also in the study of quantization first envisaged by Hermann Weyl thirty years earlier.