scholarly journals On a symbol class of elliptic pseudodifferential operators

2002 ◽  
Vol 123 (27) ◽  
pp. 57-68 ◽  
Author(s):  
Stevan Pilipovic ◽  
Nenad Teofanov
Keyword(s):  
Phase Space ◽  
Polynomial Growth ◽  
Pseudodifferential Operators ◽  
Growth Conditions ◽  
Modulation Spaces ◽  
Bessel Potentials ◽  
Weyl Transforms ◽  
Symbol Class

We consider a class of symbols with prescribed smoothness and growth conditions and give examples of such symbols. The introduced class contains certain polynomial symbols and symbols with more, than polynomial growth in phase space. The corresponding pseudodifferential operators defined as the Weyl transforms of the symbols are elliptic. As an application, we give a result on isomorphisms between modulation spaces. In particular, we show that the Bessel potentials establish such isomorphisms.

scholarly journals Schatten p-class property of pseudodifferential operators with symbols in modulation spaces

2012 ◽  
Vol 205 ◽  
pp. 119-148
Author(s):  
Masaharu Kobayashi ◽  
Akihiko Miyachi
Keyword(s):  
Pseudodifferential Operators ◽  
Modulation Spaces

AbstractIt is proved that the pseudodifferential operators σt(X, D) belong to the Schatten p-class Cp, 0 < p ≤ 2, if the symbol σ(x,ω) is in certain modulation spaces on

ON MARTINEZ’ METHOD OF PHASE SPACE TUNNELING

1995 ◽  
Vol 07 (03) ◽  
pp. 431-441 ◽  
Author(s):  
SHU NAKAMURA
Keyword(s):  
Phase Space ◽  
Pseudodifferential Operators

A generalization of the method of martinez on phase space tunneling is discussed. In particular, the key estimate is formulated for a class of ħ-pseudodifferential operators.

scholarly journals Schatten p-class property of pseudodifferential operators with symbols in modulation spaces

2012 ◽  
Vol 205 ◽  
pp. 119-148
Author(s):  
Masaharu Kobayashi ◽  
Akihiko Miyachi
Keyword(s):  
Pseudodifferential Operators ◽  
Modulation Spaces

AbstractIt is proved that the pseudodifferential operatorsσt(X, D) belong to the Schattenp-classCp, 0&lt; p≤ 2, if the symbolσ(x,ω) is in certain modulation spaces on

scholarly journals Approximating graphs with polynomial growth

2000 ◽  
Vol 42 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Norbert Seifter ◽  
Wolfgang Woess
Keyword(s):  
Inverse Limit ◽  
Polynomial Growth ◽  
Infinite Sequence ◽  
Growth Conditions ◽  
Infinite Graph ◽  
Subject Classification ◽  
Transitive Graph ◽  
Locally Finite ◽  
Finite Graphs ◽  
Growth Properties

Let X be an infinite, locally finite, almost transitive graph with polynomial growth. We show that such a graph X is the inverse limit of an infinite sequence of finite graphs satisfying growth conditions which are closely related to growth properties of the infinite graph X.1991 Mathematics Subject Classification. Primary 05C25, Secondary 20F8.

scholarly journals QUANTUM-DEFORMED CANONICAL TRANSFORMATIONS, W∞ ALGEBRAS AND UNITARY TRANSFORMATIONS

1994 ◽  
Vol 09 (32) ◽  
pp. 5801-5820 ◽  
Author(s):  
E. GOZZI ◽  
M. REUTER
Keyword(s):  
Phase Space ◽  
Pseudodifferential Operators ◽  
Star Product ◽  
Canonical Transformations ◽  
Symbol Calculus ◽  
Algebra Of Functions ◽  
Unitary Transformations ◽  
Symbols Of Operators ◽  
Left And Right ◽  
Gns Construction

We investigate the algebraic properties of the quantum counterpart of the classical canonical transformations using the symbol calculus approach to quantum mechanics. In this framework we construct a set of pseudodifferential operators which act on the symbols of operators, i.e. on functions defined over phase space. They act as operatorial left and right multiplication and form a W∞×W∞ algebra which contracts to its diagonal subalgebra in the classical limit. We also describe the Gel’fand-Naimark-Segal (GNS) construction in this language and show that the GNS representation space (a doubled Hilbert space) is closely related to the algebra of functions over phase space equipped with the star product of the symbol calculus.

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