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2013
Pseudo-differential operators are important generalization of differential operators. These operators were first introduced in 1960 by Friedrichs and Lax in the study of singular integral differential operators, mainly, for inverting differential operators to solve differential equations.
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Pseudo-differential operators are important generalization of differential operators. These operators were first introduced in 1960 by Friedrichs and Lax in the study of singular integral differential operators, mainly, for inverting differential operators to solve differential equations.
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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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Bopp Pseudo-differential Operators
2011Bopp pseudo-differential operators are the operators formally obtained from a symbol by the quantization rules $$x \to x + \frac{1} {2}i\rlap{--} h\partial _{p\,} \,,\,\,p \to p - \frac{1} {2}i\rlap{--} h\partial _x$$ (18.1) instead of the usual correspondence\(x \to x,\,p\, \to \, - i\rlap{--} h\partial _{x.}\) The terminology comes from the
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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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Sampling and Pseudo-Differential Operators
2008Discrete formulas for pseudo-differential operators based on the Shannon-Whittaker sampling formula and the Poisson summation formula are given.
Alip Mohammed, M. W. Wong
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