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ON THE MICROLOCAL STRUCTURE OF PSEUDODIFFERENTIAL OPERATORS
Mathematics of the USSR-Sbornik, 1987The authors consider the classical pseudodifferential operators (p.d.o.) on the smooth manifold M. The operators \(\hat H_ 1=H_ 1(x,-i\partial /\partial x)\) and \(\hat H_ 2=H_ 2(x,-i\partial/\partial x)\) are microlocal equivalent at the point \((x_ 0,p_ 0)\in T^*_ 0(M)\) if there exist an elliptic Fourier integral operator \({\hat\Phi}\), associated ...
Lychagin, V. V., Sternin, B. Yu.
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Pseudodifferential Operators as Integral Operators
2021All of the integral operators with nonintegrable kernels are given in terms of computable Hadamard's partie finie, i.e. finite part integrals [168], which can be applied to problems in applications (Guiggiani [163], Schwab et al [380]).
George C. Hsiao, Wolfgang L. Wendland
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PSEUDODIFFERENTIAL OPERATORS OF PRINCIPAL TYPE
Mathematics of the USSR-Sbornik, 1967Let P(D) be a differential operator of order m with constant coefficients, and let P0(ξ) be its principal symbol.
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Pseudodifferential Operators and Linear Connections
Proceedings of the London Mathematical Society, 1997The aim of the paper is to construct a calculus of pseudodifferential operators (PDOs) on a smooth manifold \(M\) without using local coordinate systems. Instead we deal with linear connections \(\Gamma\) of \(M\). The fact that a linear connection \(\Gamma\) is a global object enables one to associate with a PDO its full symbol, which is a function on
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NONDEGENERATE SUBELLIPTIC PSEUDODIFFERENTIAL OPERATORS
Mathematics of the USSR-Sbornik, 1970In this paper we study scalar pseudodifferential operators for which the gradient of the principal part of the symbol does not vanish and is not proportional to a real vector at any characteristic point . Such operators are called nondegenerate. It is assumed in addition that for each point of there exists an operator in the Lie algebra generated by ...
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A Pedestrian’s Approach to Pseudodifferential Operators
2007Pseudodifferential operators are an indispensable tool for the study of partial differential equations and are therefore a branch of classical analysis. In this chapter we offer an approach using time-frequency methods. In this approach time-frequency representations that are standard in signal analysis are used to set up the formalism of ...
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