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Nonregular Pseudo-Differential Operators
Zeitschrift für Analysis und ihre Anwendungen, 1996We study the boundedness properties of pseudo-differential operators a(x, D) and their adjoints a(x, D)* with symbols in a certain vector-valued Besov space on Besov
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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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On Eigenvalues of Pseudo-Differential Operators
Bulletin of the London Mathematical Society, 1987Conditions are given to ensure the existence and finiteness of the number of eigenvalues below the essential spectrum of self-adjoint realizations H of the operator \((D^ 2+m^ 2)^{1/2}+q(x)\) in \(L^ 2({\mathbb{R}}^ n)\) \((D=-i\partial /\partial x\), \(m>0\) a constant, q real valued).
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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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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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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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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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Pseudo-Differential Operators of Principal Type
1981In Section 10.4 we saw that the strength of a differential operator with constant coefficients in ℝ n is determined by the principal part p if and only if p=0 implies dp≠0 in ℝ n \0. Such operators were said to be of principal type. The purpose of this chapter is to study general operators P∈Ψ phg m (X) on a manifold X assuming that the condition dp ≠0
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Theory of Pseudo-differential Operators
2004In this chapter we present a brief description of the basic concepts and results from the theory of pseudo-differential operators – a modern theory of potentials –which will be used in the subsequent chapters. The development of the theory of pseudo-differential operators has greatly advanced our understanding of partial differential equations, and the
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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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