Hörmander, L., The Analysis of Linear Partial Differential Operators IV: Fourier Integral Operators. Berlin-Heidelberg-New York-Tokyo, Springer-Verlag 1985. VII, 352 S., DM 128,–. ISBN 3-540-13829-3 (Grundlehren der mathematischen Wissenschaften 275)

1987 ◽  
Vol 67 (11) ◽  
pp. 579-579
Author(s):  
G. Anger
Keyword(s):  
New York ◽  
Differential Operators ◽  
Integral Operators ◽  
Fourier Integral ◽  
Fourier Integral Operators ◽  
Partial Differential ◽  
Partial Differential Operators ◽  
Linear Partial Differential Operators

scholarly journals Generalized oscillatory integrals and Fourier integral operators

2009 ◽  
Vol 52 (2) ◽  
pp. 351-386 ◽  
Author(s):  
Claudia Garetto ◽  
Günther Hörmann ◽  
Michael Oberguggenberger
Keyword(s):  
Differential Operators ◽  
Integral Operators ◽  
Fourier Integral ◽  
Generalized Functions ◽  
Oscillatory Integrals ◽  
Fourier Integral Operators ◽  
Partial Differential Operators ◽  
Colombeau Algebras ◽  
Smooth Coefficients ◽  
Phase Functions

AbstractIn this paper, a theory is developed of generalized oscillatory integrals (OIs) whose phase functions and amplitudes may be generalized functions of Colombeau type. Based on this, generalized Fourier integral operators (FIOs) acting on Colombeau algebras are defined. This is motivated by the need for a general framework for partial differential operators with non-smooth coefficients and distribution dataffi The mapping properties of these FIOs are studied, as is microlocal Colombeau regularity for OIs and the influence of the FIO action on generalized wavefront sets.

The Calder´on-Zygmund Theory I: Ellipticity

2017 ◽  
Author(s):  
Brian Street
Keyword(s):  
Classical Theory ◽  
Singular Integral ◽  
Singular Integrals ◽  
Differential Operators ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Single Parameter ◽  
Partial Differential ◽  
Translation Invariant ◽  
Partial Differential Operators

This chapter discusses a case for single-parameter singular integral operators, where ρ‎ is the usual distance on ℝn. There, we obtain the most classical theory of singular integrals, which is useful for studying elliptic partial differential operators. The chapter defines singular integral operators in three equivalent ways. This trichotomy can be seen three times, in increasing generality: Theorems 1.1.23, 1.1.26, and 1.2.10. This trichotomy is developed even when the operators are not translation invariant (many authors discuss such ideas only for translation invariant, or nearly translation invariant operators). It also presents these ideas in a slightly different way than is usual, which helps to motivate later results and definitions.

Sign in / Sign up

Export Citation Format

Share Document