On the Characterization of Pseudodifferential Operators (Old and New)

2013 ◽  
pp. 21-34
Author(s):  
Jean-Michel Bony
Keyword(s):  
Pseudodifferential Operators

scholarly journals Properties of the algebra Psd related to integrable hierarchies

2020 ◽  
pp. 183-195
Author(s):  
Gerard F. Helminck ◽  
Elena A. Panasenko
Keyword(s):  
Integrable Hierarchies ◽  
Pseudodifferential Operators ◽  
Darboux Transformations ◽  
Fredholm Determinants

In this paper we discuss and prove various properties of the algebra of pseudodifferential operators related to integrable hierarchies in this algebra, in particular the KPhierarchy and its strict version. Some explain the form of the equations involved or giveinsight in why certain equations in these systems are combined, others lead to additionalproperties of these systems like a characterization of the eigenfunctions of the linearizations ofthe mentioned hierarchies, the description of elementary Darboux transformations of bothhierarchies and the search for expressions in Fredholm determinants for the constructedeigenfunctions and their duals.

scholarly journals On duality theory and pseudodifferential techniques for Colombeau algebras: generalized delta functionals, kernels and wave front sets

2006 ◽  
Vol 133 (31) ◽  
pp. 115-136 ◽  
Author(s):  
Claudia Garetto ◽  
G. Hormann
Keyword(s):  
Wave Front ◽  
Pseudodifferential Operators ◽  
Symbol Calculus ◽  
Wave Front Set ◽  
Colombeau Algebras ◽  
Generalized Complex Numbers ◽  
Topological Modules ◽  
Wave Front Sets ◽  
Basic Facts

Summarizing basic facts from abstract topological modules over Colombeau generalized complex numbers we discuss duality of Colombeau algebras. In particular, we focus on generalized delta functional and operator kernels as elements of dual spaces. A large class of examples is provided by pseudodifferential operators acting on Colombeau algebras. By a refinement of symbol calculus we review a new characterization of the wave front set for generalized functions with applications to microlocal analysis. AMS Mathematics Subject Classification (2000): 46F30, 46A20, 47G30.

scholarly journals Beals Characterization of Pseudodifferential Operators in Wiener Spaces

2016 ◽  
pp. abw001 ◽  
Author(s):  
Laurent Amour ◽  
Richard Lascar ◽  
Jean Nourrigat
Keyword(s):  
Pseudodifferential Operators ◽  
Wiener Spaces

scholarly journals A groupoid approach to pseudodifferential calculi

2019 ◽  
Vol 2019 (756) ◽  
pp. 151-182 ◽  
Author(s):  
Erik van Erp ◽  
Robert Yuncken
Keyword(s):  
Pseudodifferential Operator ◽  
Tangent Bundle ◽  
Smooth Manifold ◽  
Pseudodifferential Operators ◽  
Geometric Characterization ◽  
Smooth Functions ◽  
Schwartz Kernel ◽  
Basic Properties ◽  
Family Of Distributions

AbstractIn this paper we give an algebraic/geometric characterization of the classical pseudodifferential operators on a smooth manifold in terms of the tangent groupoid and its natural {\mathbb{R}^{\times}_{+}}-action. Specifically, a properly supported semiregular distribution on {M\times M} is the Schwartz kernel of a classical pseudodifferential operator if and only if it extends to a smooth family of distributions on the range fibers of the tangent groupoid that is homogeneous for the {\mathbb{R}^{\times}_{+}}-action modulo smooth functions. Moreover, we show that the basic properties of pseudodifferential operators can be proven directly from this characterization. Further, with the appropriate generalization of the tangent bundle, the same definition applies without change to define pseudodifferential calculi on arbitrary filtered manifolds, in particular the Heisenberg calculus.

scholarly journals Characterization of Non-Smooth Pseudodifferential Operators

2017 ◽  
Vol 24 (2) ◽  
pp. 371-415 ◽  
Author(s):  
Helmut Abels ◽  
Christine Pfeuffer
Keyword(s):  
Pseudodifferential Operators

Morphological Characterization of Mycobacteriophage R1

1974 ◽  
Vol 32 ◽  
pp. 254-255
Author(s):  
B. L. Soloff ◽  
T. A. Rado
Keyword(s):  
Carbon Source ◽  
Stationary Phase ◽  
Growth Phase ◽  
Minimal Medium ◽  
Morphological Characterization ◽  
Logarithmic Growth Phase ◽  
Complete Lysis ◽  
Lysogenic Culture ◽  
Logarithmic Growth

Mycobacteriophage R1 was originally isolated from a lysogenic culture of M. butyricum. The virus was propagated on a leucine-requiring derivative of M. smegmatis, 607 leu−, isolated by nitrosoguanidine mutagenesis of typestrain ATCC 607. Growth was accomplished in a minimal medium containing glycerol and glucose as carbon source and enriched by the addition of 80 μg/ ml L-leucine. Bacteria in early logarithmic growth phase were infected with virus at a multiplicity of 5, and incubated with aeration for 8 hours. The partially lysed suspension was diluted 1:10 in growth medium and incubated for a further 8 hours. This permitted stationary phase cells to re-enter logarithmic growth and resulted in complete lysis of the culture.

Sign in / Sign up

Export Citation Format

Share Document