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Quantization and Arithmetic (Paperback, 2008 ed.)
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Quantization and Arithmetic (Paperback, 2008 ed.)
Series: Pseudo-Differential Operators, 1
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(12) (4) Let ? be the unique even non-trivial Dirichlet character
mod 12, and let ? be the unique (odd) non-trivial Dirichlet
character mod 4. Consider on the line the distributions m (12) ? d
(x)= ? (m)? x? , even 12 m?Z m (4) d (x)= ? (m)? x? . (1.1) odd 2
m?Z 2 i?x
UnderaFouriertransformation,orundermultiplicationbythefunctionx ? e
, the?rst(resp.
second)ofthesedistributionsonlyundergoesmultiplicationbysome 24th
(resp. 8th) root of unity. Then, consider the metaplectic
representation Met, 2 a unitary representation in L (R) of the
metaplectic group G, the twofold cover of the group G = SL(2,R),
the de?nition of which will be recalled in Section 2: it extends as
a representation in the spaceS (R) of tempered distributions. From
what has just been said, if g ~ is a point of G lying above g?
G,andif d = d even g ~ ?1 or d , the distribution d =Met(g~ )d only
depends on the class of g in the odd
homogeneousspace?\G=SL(2,Z)\G,uptomultiplicationbysomephasefactor,
by which we mean any complex number of absolute value 1 depending
only on g ~. On the other hand, a function u?S(R) is perfectly
characterized by its scalar g ~ productsagainstthedistributionsd
,sinceonehasforsomeappropriateconstants C , C the identities 0 1 g
~ 2 2 | d ,u | dg = C u if u is even, 2 0 even L (R) ?\G
General
Imprint: |
Birkhauser Verlag AG
|
Country of origin: |
Switzerland |
Series: |
Pseudo-Differential Operators, 1 |
Release date: |
June 2008 |
First published: |
2008 |
Authors: |
Andr e Unterberger
|
Dimensions: |
240 x 170 x 8mm (L x W x T) |
Format: |
Paperback
|
Pages: |
147 |
Edition: |
2008 ed. |
ISBN-13: |
978-3-7643-8790-7 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
General
|
LSN: |
3-7643-8790-4 |
Barcode: |
9783764387907 |
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