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1997
The theory of pseudo-differential operators is one of the most important toolsin modern mathematics. It has found important applications in many mathematicaldevelopments. It was used in a crucial way in the proof of the Atiyah-SingerIndex theorem in [AtSi] and in the regularity of elliptic differential equations.In the theory of several complex ...
Yuri V. Egorov, Bert-Wolfgang Schulze
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The theory of pseudo-differential operators is one of the most important toolsin modern mathematics. It has found important applications in many mathematicaldevelopments. It was used in a crucial way in the proof of the Atiyah-SingerIndex theorem in [AtSi] and in the regularity of elliptic differential equations.In the theory of several complex ...
Yuri V. Egorov, Bert-Wolfgang Schulze
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Communications on Pure and Applied Mathematics, 1965
Contents: Second Order Elliptic Operators.- Pseudo-Differential Operators.- Elliptic Operators on a Compact Manifold without Boundary.- Boundary Problems for Elliptic Differential Operators.- Symplectic Geometry.- Some Classes of (Micro-)Hypoelliptic Operators.- The Strictly Hyperbolic Cauchy Problem.- The Mixed Dirichlet-Cauchy Problem for Second ...
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Contents: Second Order Elliptic Operators.- Pseudo-Differential Operators.- Elliptic Operators on a Compact Manifold without Boundary.- Boundary Problems for Elliptic Differential Operators.- Symplectic Geometry.- Some Classes of (Micro-)Hypoelliptic Operators.- The Strictly Hyperbolic Cauchy Problem.- The Mixed Dirichlet-Cauchy Problem for Second ...
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1985
We will now turn to a class of operators which — roughly speaking (details below) — are locally presentable in the form $$\left( {Pu} \right)\left( x \right)\,: = \int {ei p\left( {x,\varepsilon } \right)} \mathop u\limits^ \wedge \left( \varepsilon \right)d\varepsilon$$ where $$ \hat u\left( x \right): = \int {e^{ - i\left\langle {x,\xi }
B. Booss, D. D. Bleecker
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We will now turn to a class of operators which — roughly speaking (details below) — are locally presentable in the form $$\left( {Pu} \right)\left( x \right)\,: = \int {ei p\left( {x,\varepsilon } \right)} \mathop u\limits^ \wedge \left( \varepsilon \right)d\varepsilon$$ where $$ \hat u\left( x \right): = \int {e^{ - i\left\langle {x,\xi }
B. Booss, D. D. Bleecker
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2010
The main purpose of this chapter is to obtain the boundedness on \(A_{p, q}^{s, \tau }({\mathbb{R}}^ n)\) of all pseudo-differential operators of type (1,1) with inhomogeneous symbols. The smooth molecular decomposition characterizations of \(A_{p, q}^{s, \tau }({\mathbb{R}}^ n)\) play an important role in this chapter.
Wen Yuan, Winfried Sickel, Dachun Yang
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The main purpose of this chapter is to obtain the boundedness on \(A_{p, q}^{s, \tau }({\mathbb{R}}^ n)\) of all pseudo-differential operators of type (1,1) with inhomogeneous symbols. The smooth molecular decomposition characterizations of \(A_{p, q}^{s, \tau }({\mathbb{R}}^ n)\) play an important role in this chapter.
Wen Yuan, Winfried Sickel, Dachun Yang
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Annali di Matematica Pura ed Applicata, 1972
We present here a number of results on some aspects of Kohn-Nirenberg's theory of pseudo-differential operators. We hope that some parts of Kohn-Nirenberg's paper[1] are presented here in a more detailed and explicit form; this could help a larger audience to understand their ideas and methods.
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We present here a number of results on some aspects of Kohn-Nirenberg's theory of pseudo-differential operators. We hope that some parts of Kohn-Nirenberg's paper[1] are presented here in a more detailed and explicit form; this could help a larger audience to understand their ideas and methods.
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G-Pseudo-Differential Operators
2010As in Chapter 2, the basic example here is a partial differential operator with polynomial coefficients in ℝ d , that is $$ P = \sum {c_{\alpha \beta } x^\beta D^\alpha } , $$ wherein the sum (α,β) ∈ ℕ d × ℕ d runs over a finite subset of indices.
Fabio Nicola, Luigi Rodino
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Bounded pseudo-differential operators
Israel Journal of Mathematics, 1972This lecture gives an inside look into the proof of the continuity of pseudo-differential operators of orderm and typep, δ1, δ2 for 0≦p≦δ1=1, 0≦p ...
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Elliptic pseudo-differential operators
1997A pseudo-differential operator P with a symbol p ∈ S m (Ω) is elliptic in Ω, if for any compact subset K ⊂ Ω there exist positive constants c and C such that p(x,ξ)≥cξ m for ξ ...
Yuri V. Egorov, Bert-Wolfgang Schulze
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Gel'Fand Theory of Pseudo Differential Operators
American Journal of Mathematics, 1968Introduction. The conventional pseudo differential operators were introduced by Kohn and Nirenberg [8] and extensively studied in a generalized version by Hdrmander [7]. In either case they appear as operators acting on C, -functions of a differentiable manifold; their definition is designed to obtain a class of linear operators containing all linear ...
Cordes, H. O., Herman, E. A.
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Finite pseudo-differential operators
Journal of Pseudo-Differential Operators and Applications, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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