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Pseudodifferential Operators
"... In this chapter we discuss the basic theory of pseudodifferential operators as it has been developed to treat problems in linear PDE. We define pseudodifferential operators with symbols in classes denoted Sm ρ,δ, introduced ..."
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In this chapter we discuss the basic theory of pseudodifferential operators as it has been developed to treat problems in linear PDE. We define pseudodifferential operators with symbols in classes denoted Sm ρ,δ, introduced
Pseudodifferential Operators
, 2004
"... The study of pseudodifferential operators emerged in the 1960’s, having its origins in the study of singular integrodifferential operators. In fact, Friedrichs and Lax coined the term “pseudodifferential operator ” in their 1965 paper entitled “Boundary Value Problems for First Order Operators”. Si ..."
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The study of pseudodifferential operators emerged in the 1960’s, having its origins in the study of singular integrodifferential operators. In fact, Friedrichs and Lax coined the term “pseudodifferential operator ” in their 1965 paper entitled “Boundary Value Problems for First Order Operators
On Pseudodifferential Operators by:
, 2004
"... In this paper we present a brief survey of several topics and applications of the theory of pseudodifferential operators. First, we define a pseudodifferential operator when the underlying space is the Euclidean space. We discuss the main properties of pseudodifferential operators, and then we exten ..."
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In this paper we present a brief survey of several topics and applications of the theory of pseudodifferential operators. First, we define a pseudodifferential operator when the underlying space is the Euclidean space. We discuss the main properties of pseudodifferential operators, and then we
Pseudodifferential operators on differential groupoids
 Pacific J. Math
, 1999
"... We construct an algebra of pseudodifferential operators on each groupoid in a class that generalizes differentiable groupoids to allow manifolds with corners. We show that this construction encompasses many examples. The subalgebra of regularizing operators is identified with the smooth algebra of t ..."
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Cited by 71 (7 self)
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We construct an algebra of pseudodifferential operators on each groupoid in a class that generalizes differentiable groupoids to allow manifolds with corners. We show that this construction encompasses many examples. The subalgebra of regularizing operators is identified with the smooth algebra
Pseudodifferential Operators of Infinite Order
"... In this note we establish a formula which gives quantized contact transformations of pseudodifferential operators in terms of symbols. A quantization of a given cont act transformation $\phi $ is an extension of $\phi $ to a ring isomorphism $\phi_{*} $ between the rings of pseudodifferential oper ..."
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In this note we establish a formula which gives quantized contact transformations of pseudodifferential operators in terms of symbols. A quantization of a given cont act transformation $\phi $ is an extension of $\phi $ to a ring isomorphism $\phi_{*} $ between the rings of pseudodifferential
Pseudodifferential operators and regularized traces
, 2009
"... This is a survey on trace constructions on various operator algebras with an emphasis on regularized traces on algebras of pseudodifferential operators. For motivation our point of departure is the classical Hilbert space trace which is the unique semifinite normal trace on the algebra of bounded ..."
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Cited by 7 (0 self)
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This is a survey on trace constructions on various operator algebras with an emphasis on regularized traces on algebras of pseudodifferential operators. For motivation our point of departure is the classical Hilbert space trace which is the unique semifinite normal trace on the algebra of bounded
Lp CONTINUITY FOR PSEUDODIFFERENTIAL OPERATORS
"... It is well known in the classical literature that the pseudodifferential operators with symbols in the Hörmander classes S0ρ,δ are not in general L p bounded when ρ < 1, but a loss of regularity occurs. We can obtain exactly Lp continuity by adding suitable conditions to the symbol classes which ..."
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It is well known in the classical literature that the pseudodifferential operators with symbols in the Hörmander classes S0ρ,δ are not in general L p bounded when ρ < 1, but a loss of regularity occurs. We can obtain exactly Lp continuity by adding suitable conditions to the symbol classes
Magnetic Pseudodifferential operators with coefficients
 in C ∗  algebras, preprint arXiv 0901.3704 and submitted
"... In previous articles, a magnetic pseudodifferential calculus and a family of C ∗algebras associated with twisted dynamical systems were introduced and the connections between them have been established. We extend this formalism to symbol classes of Hörmander type with an xbehavior modelized by an ..."
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Cited by 11 (4 self)
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by an abelian C ∗algebra. Some of these classes generate C ∗algebras associated with the twisted dynamical system. We show the relevance of these classes to the spectral analysis of pseudodifferential operators with anisotropic symbols and magnetic fields.
Results 1  10
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953