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Periodic Pseudodifferential Operators
2002In this chapter we present a systematic theory of periodic pseudodifferential operators. In next chapters the pseudodifferential structure of periodic integral operators will be extensively used by constructing fast solvers for integral equations.
Jukka Saranen, Gennadi Vainikko
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Standard Pseudodifferential Operators
1980This chapter is the basic one in the book and, I hope, the most elementary. Its contents are essentially the definitions and fundamental properties of what are called here standard pseudodifferential operators, often called operators of type (1, 0), to contrast them with operators of type (ρ, δ), studied in Chapter IV. The presentation follows the line
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Analytic Pseudodifferential Operators
1980“Generalized functions,” playing the role vis-a-vis analytic functions that distributions play vis-a-vis C ∞ functions, do exist: They are the hyper-functions of M. Sato. The analogues of pseudodifferential (and even hyperdifferential) operators can be made to act on them, and many results in this book have hyperfunction parallels. On this vast subject
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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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Meromorphic pseudodifferential operators
1989Meromorphic pseudodifferential operators arise, e.g., after applying the Mellin transform on the right and on the left to the operator of convolution with a homogeneous function. A ‘canonical’ meromorphic pseudodifferential operator of order a has the form E θ→o (λ + ia)-1Ф(o, θ)E Ψ→θ (λ).
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Analytic Pseudodifferential Operators
2017The theory of analytic pseudo-differential operators (hereafter abbreviated as ψDOs) started with [BKr67]. The interest of Professor Boutet de Monvel in analyticity is characteristic in his research, and it is remarkable as “regularity” normally meant C ∞ in 1960s.
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