Remarks on pseudo-differential operators*
نویسندگان
چکیده
منابع مشابه
Remarks on Quantum Differential Operators
In the course of writing the book [9] and various papers [10, 11, 12, 13, 14, 15, 16] we encountered many q-differential equations but were frustrated by a lack of understanding about natural forms for such equations. One has operators of the type qKP or qKdV for example but even there, expressing the resulting equations (even via Hirota type equations or in bilinear form) seemed curiously diff...
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We define and study pseudo-differential operators on a class of fractals that include the post-critically finite self-similar sets and Sierpinski carpets. Using the sub-Gaussian estimates of the heat operator we prove that our operators have kernels that decay and, in the constant coefficient case, are smooth off the diagonal. Our analysis can be extended to product of fractals. While our resul...
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For recent developments of this work in the classical direction, especially to generalizing to modular groups acting on higher dimensional spaces, see papers of Min Ho Lee: http://www.math.uni.edu/ lee/pub.html. He has, for example, developed the Hilbert modular case. Also, Olav Richter’s work on Rankin-Cohen brackets: http://www.math.unt.edu/ richter/. Work of Conley on 1/2-integral weight: ht...
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In this paper we study properties of symbols such that these belong to class of symbols sitting insideSm ρ,φ that we shall introduce as the following. So for because hypoelliptic pseudodifferential operatorsplays a key role in quantum mechanics we will investigate some properties of M−hypoelliptic pseudodifferential operators for which define base on this class of symbols. Also we consider maxi...
متن کاملIntroduction to pseudo-differential operators
The present notes give introduction to the theory of pseudo-differential operators on Euclidean spaces. The first part is devoted to the necessary analysis of functions, such as basics of the Fourier analysis and the theory of distributions and Sobolev spaces. The second part is devoted to pseudo-differential operators and their applications to partial differential equations. We refer to the mo...
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1969
ISSN: 0025-5645
DOI: 10.2969/jmsj/02130413