Download Alternative Pseudodifferential Analysis: With an Application by André Unterberger PDF

By André Unterberger

ISBN-10: 3540779108

ISBN-13: 9783540779100

ISBN-10: 3540779116

ISBN-13: 9783540779117

This quantity introduces a completely new pseudodifferential research at the line, the competition of which to the standard (Weyl-type) research may be stated to mirror that, in illustration concept, among the representations from the discrete and from the (full, non-unitary) sequence, or that among modular kinds of the holomorphic and alternative for the standard Moyal-type brackets. This pseudodifferential research depends on the one-dimensional case of the lately brought anaplectic illustration and research, a competitor of the metaplectic illustration and traditional analysis.

Besides researchers and graduate scholars drawn to pseudodifferential research and in modular types, the e-book can also entice analysts and physicists, for its innovations making attainable the transformation of creation-annihilation operators into automorphisms, concurrently altering the standard scalar product into an indefinite yet nonetheless non-degenerate one.

Show description

Read Online or Download Alternative Pseudodifferential Analysis: With an Application to Modular Forms PDF

Similar group theory books

Groups and Symmetry: A Guide to Discovering Mathematics (Mathematical World, Volume 5)

In so much arithmetic textbooks, the main interesting a part of mathematics--the strategy of invention and discovery--is thoroughly hidden from the reader. the purpose of teams and Symmetry is to alter all that. through a chain of rigorously chosen projects, this ebook leads readers to find a few genuine arithmetic.

Groups of Finite Morley Rank

This ebook essentially info the idea of teams of finite Morley rank--groups which come up in version concept and generalize the concept that of algebraic teams over algebraically closed fields. Written in particular for natural staff theorists and graduate scholars embarking on learn at the topic, the ebook develops the idea from the start and comprises an algebraic and self-evident instead of a model-theoretic standpoint.

Extra resources for Alternative Pseudodifferential Analysis: With an Application to Modular Forms

Example text

57) when ε = 0, this is a representation taken from the complementary series of SL(2, R); when ε = 1, it is a signed version, non unitarizable, of the same. More details can be found in [38, Sect. 2], with the same notation. 12. Under the map u → ((Q u)0 , (Q u)1 ), the anaplectic representation transfers to the representation (πˆ− 1 ,0 , πˆ 1 ,1 ). 2 2 Proof. Though it is contained in the above given reference, let us at least give a short indication about one of the possible proofs of the proposition.

6 should continue to hold. 4 is still valid. Let us set (the first item is just a notational convenience) δ0m+1 = 1 ∂ , π ∂z δ1m+1 = 1 ∂ (z + m + 1). 36) 44 3 The One-Dimensional Alternative Pseudodifferential Analysis What we want to do is to define B = Opasc (i w) ¯ α 1 ∂ π ∂w β fm−α −β as B = [Q, [Q, . . [P, [P, . . , Opasc m−α −β ( f m−α −β )] . . ] . . 37) where the number of Q ’s is α and the number of P ’s is β . 6, this equation is correct in the case when fm−α −β ∈ Sm (R2 ). 34), setting χm−α −β +1 = Θm−α −β hm−α −β and considering an arbitrary sequence (ε1 , .

Finding a symbolic 2 calculus of operators, covariant under the anaplectic representation, quite appropriately started from the consideration of a calculus of operators based on the use of Hi as a temporary phase space. The corresponding quantization program, including a study of the sharp composition of symbols, was implemented in [34]; the quantizing map, in that case, had independently been obtained in [22]. In the present investigations, special consideration is attached to the discrete part only of the decomposition of L2 (Hi ).

Download PDF sample

Alternative Pseudodifferential Analysis: With an Application to Modular Forms by André Unterberger

by Mark

Rated 4.90 of 5 – based on 46 votes