Theory of p-adic distributions: linear and nonlinear models
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2010
|
| Edition: | 1. publ. |
| Series: | London Mathematical Society lecture note series
370 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 351 S. |
| ISBN: | 9780521148566 0521148561 |
Staff View
MARC
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| 100 | 1 | |a Albeverio, Sergio |d 1939- |e Verfasser |0 (DE-588)121093999 |4 aut | |
| 245 | 1 | 0 | |a Theory of p-adic distributions |b linear and nonlinear models |c S. Albeverio ; A. Yu Khrennikov ; V. M. Shelkovich |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2010 | |
| 300 | |a XVI, 351 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a London Mathematical Society lecture note series |v 370 | |
| 650 | 4 | |a Distribution (Probability theory) | |
| 650 | 4 | |a p-adic analysis | |
| 650 | 4 | |a p-adic numbers | |
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| 650 | 0 | 7 | |a Pseudodifferentialgleichung |0 (DE-588)4121533-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a p-adische Analysis |0 (DE-588)4252360-6 |2 gnd |9 rswk-swf |
| 653 | |a p-adic analysis | ||
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| 700 | 1 | |a Khrennikov, Andrei |d 1958- |e Verfasser |0 (DE-588)128568410 |4 aut | |
| 700 | 1 | |a Šelkovič, Vladimir M. |e Verfasser |0 (DE-588)128568445 |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-019014929 | ||
Record in the Search Index
| _version_ | 1804141234055282688 |
|---|---|
| adam_text | Contents
Preface
page
xi
1
/j-adic numbers
1
1.1
Introduction
1
1.2
Archimedean and
non-
Archimedean normed fields
1
.3
Metrics and norms on the field of rational numbers
6
.4
Construction of the completion of a normed field
10
.5
Construction of the field of /7-adic numbers Qp
14
.6
Canonical expansion of p-adic numbers
15
.7
The ring of p-adic integers Zp
19
.8
Non-Archimedean topology of the field Qp
21
.9
Qp in connection with
К
25
.10
The space
ψρ
33
2
p-adic functions
35
2.1
Introduction
35
2.2 p-aäic
power series
35
2.3
Additive and multiplicative characters of the field Qp
40
3
p-adic integration theory
47
3.1
Introduction
47
3.2
The
Haar
measure and integrals
47
3.3
Some simple integrals
51
3.4
Change of variables
52
4
p-adic distributions
54
4.1
Introduction
54
4.2
Locally constant functions
54
4.3
The Brahat-Schwartz test functions
56
4.4
The Brahat-Schwartz distributions (generalized functions)
58
4.5
The direct product of distributions
63
vii
viii Contents
4.6
The Schwartz kernel theorem
64
4.7
The convolution of distributions
65
4.8
The Fourier transform of test functions
68
4.9
The Fourier transform of distributions
71
5
Some results from p-adic
£ -
and £2-theories
75
5.1
Introduction
5
5.2
Cl -theory 75
5.3
^-theory 77
6
The theory of associated and quasi associated homogeneous
p-adic distributions
80
6.1
Introduction
80
6.2
p-adic homogeneous distributions
80
6.3
p-adic quasi associated homogeneous distributions
83
6.4
The Fourier transform of p-adic quasi associated homogeneous
distributions
93
6.5
New type of p-adic
Γ
-functions
94
7
p-adic Lizorkin spaces of test functions and distributions
97
7.1
Introduction
97
7.2
The real case of Lizorkin spaces
98
7.3
p-adic Lizorkin spaces
99
7.4
Density of the Lizorkin spaces of test functions in
£P(<QÇ)
Ю2
8
The theory of p-adic wavelets
106
8.1
Introduction
106
8.2
p-adic
Haar
type wavelet basis via the real
Haar
wavelet basis
111
8.3
p-adic multiresolution analysis (one-dimensional case)
112
8.4
Construction of the p-adic
Haar
multiresolution analysis
115
8.5
Description of one-dimensional 2-adic
Haar
wavelet bases
121
8.6
Description of one-dimensional p-adic
Haar
wavelet bases
128
8.7
p-adic refinable functions and multiresolution analysis
140
8.8
p-adic separable multidimensional
MRA
149
8.9
Multidimensional p-adic
Haar
wavelet bases
151
8.10
One non-Haar wavelet basis in £2(QP)
155
8.11
One infinite family of non-Haar wavelet bases in £2(QP)
161
8.12
Multidimensional non-Haar p-adic wavelets
166
8.13
The p-adic Shannon-Kotelnikov theorem
168
8.14
p-adic Lizorkin spaces and wavelets
170
9
Pseudo-differential operators on the p-adic Lizorkin spaces
173
9.1
Introduction
173
9.2
p-adic multidimensional fractional operators
175
9.3
A class of pseudo-differential operators
182
9.4
Spectral theory of pseudo-differential operators
184
Contents ix
10
Pseudo-differential equations
193
10.1
Introduction
193
10.2
Simplest pseudo-differential equations
194
10.3
Linear evolutionary pseudo-differential equations of the first
order in time
197
10.4
Linear evolutionary pseudo-differential equations of the second
order in time
202
10.5
Semi-linear evolutionary pseudo-differential equations
205
11
Α ρ
-adic
Schrödinger-type
operator with point interactions
209
11.1
Introduction
209
11.2
The equation Da -XI
=
δχ
210
11.3
Definition of operator realizations of Da
+
V in £2(QP)
216
11.4
Description of operator realizations
218
11.5
Spectral properties
219
11.6
The case of ^-self-adjoint operator realizations
221
11.7
The
Friedrichs
extension
222
11.8
Two points interaction
224
11.9
One point interaction
226
12
Distributional asymptotics and p-adic Tauberian theorems
230
12.1
Introduction
230
12.2
Distributional asymptotics
231
12.3
p-adic distributional quasi-asymptotics
231
12.4
Tauberian theorems with respect to asymptotics
234
12.5
Tauberian theorems with respect to quasi-asymptotics
240
13
Asymptotics of the p-adic singular Fourier integrals
247
13.1
Introduction
247
13.2
Asymptotics of singular Fourier integrals for the real case
249
13.3
p-adic distributional asymptotic expansions
250
13.4
Asymptotics of singular Fourier integrals
(жј{х)
= 1) 251
13.5
Asymptotics of singular Fourier integrals
(πι(χ)
Џ
1) 259
13.6
p-adic version of the
Erdélyi
lemma
261
14
Nonlinear theories of p-adic generalized functions
262
14.1
Introduction
262
14.2
Nonlinear theories of distributions (the real case)
264
14.3
Construction of the p-adic Colombeau-Egorov algebra
270
14.4
Properties of Colombeau-Egorov generalized functions
272
14.5
Fractional operators in the Colombeau-Egorov algebra
276
14.6
The algebra A* of p-adic asymptotic distributions
278
14.7
A* as
a subalgebra
of the Colombeau-Egorov algebra
284
Contents
A The theory of associated and quasi associated
homogeneous real distributions
285
A.I Introduction
285
A.2 Definitions of associated homogeneous distributions and their
analysis
287
A.3 Symmetry of the class of distributions
ЛНоСЩ
295
A.4 Real quasi associated homogeneous distributions
298
A.5 Real multidimensional quasi associated homogeneous
distributions
308
A.6 The Fourier transform of real quasi associated homogeneous
distributions
313
A.7 New type of real
Γ
-functions
314
В
Two identities
317
С
Proof of a theorem on weak asymptotic expansions
319
D
One natural way to introduce a measure on Qp
331
References
333
Index
348
|
| any_adam_object | 1 |
| author | Albeverio, Sergio 1939- Khrennikov, Andrei 1958- Šelkovič, Vladimir M. |
| author_GND | (DE-588)121093999 (DE-588)128568410 (DE-588)128568445 |
| author_facet | Albeverio, Sergio 1939- Khrennikov, Andrei 1958- Šelkovič, Vladimir M. |
| author_role | aut aut aut |
| author_sort | Albeverio, Sergio 1939- |
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| classification_tum | MAT 465f MAT 428f |
| ctrlnum | (OCoLC)456170368 (DE-599)BSZ321448553 |
| dewey-full | 512.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.74 |
| dewey-search | 512.74 |
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| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV036125065 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:12:38Z |
| institution | BVB |
| isbn | 9780521148566 0521148561 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-019014929 |
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| owner_facet | DE-91G DE-BY-TUM DE-384 DE-20 DE-355 DE-BY-UBR DE-824 |
| physical | XVI, 351 S. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
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| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | London Mathematical Society lecture note series |
| series2 | London Mathematical Society lecture note series |
| spelling | Albeverio, Sergio 1939- Verfasser (DE-588)121093999 aut Theory of p-adic distributions linear and nonlinear models S. Albeverio ; A. Yu Khrennikov ; V. M. Shelkovich 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2010 XVI, 351 S. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society lecture note series 370 Distribution (Probability theory) p-adic analysis p-adic numbers Distributionstheorie (DE-588)4150254-1 gnd rswk-swf Wavelet (DE-588)4215427-3 gnd rswk-swf Pseudodifferentialgleichung (DE-588)4121533-3 gnd rswk-swf p-adische Analysis (DE-588)4252360-6 gnd rswk-swf p-adische Analysis (DE-588)4252360-6 s Wavelet (DE-588)4215427-3 s Pseudodifferentialgleichung (DE-588)4121533-3 s Distributionstheorie (DE-588)4150254-1 s DE-604 Khrennikov, Andrei 1958- Verfasser (DE-588)128568410 aut Šelkovič, Vladimir M. Verfasser (DE-588)128568445 aut London Mathematical Society lecture note series 370 (DE-604)BV000000130 370 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019014929&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Albeverio, Sergio 1939- Khrennikov, Andrei 1958- Šelkovič, Vladimir M. Theory of p-adic distributions linear and nonlinear models London Mathematical Society lecture note series Distribution (Probability theory) p-adic analysis p-adic numbers Distributionstheorie (DE-588)4150254-1 gnd Wavelet (DE-588)4215427-3 gnd Pseudodifferentialgleichung (DE-588)4121533-3 gnd p-adische Analysis (DE-588)4252360-6 gnd |
| subject_GND | (DE-588)4150254-1 (DE-588)4215427-3 (DE-588)4121533-3 (DE-588)4252360-6 |
| title | Theory of p-adic distributions linear and nonlinear models |
| title_auth | Theory of p-adic distributions linear and nonlinear models |
| title_exact_search | Theory of p-adic distributions linear and nonlinear models |
| title_full | Theory of p-adic distributions linear and nonlinear models S. Albeverio ; A. Yu Khrennikov ; V. M. Shelkovich |
| title_fullStr | Theory of p-adic distributions linear and nonlinear models S. Albeverio ; A. Yu Khrennikov ; V. M. Shelkovich |
| title_full_unstemmed | Theory of p-adic distributions linear and nonlinear models S. Albeverio ; A. Yu Khrennikov ; V. M. Shelkovich |
| title_short | Theory of p-adic distributions |
| title_sort | theory of p adic distributions linear and nonlinear models |
| title_sub | linear and nonlinear models |
| topic | Distribution (Probability theory) p-adic analysis p-adic numbers Distributionstheorie (DE-588)4150254-1 gnd Wavelet (DE-588)4215427-3 gnd Pseudodifferentialgleichung (DE-588)4121533-3 gnd p-adische Analysis (DE-588)4252360-6 gnd |
| topic_facet | Distribution (Probability theory) p-adic analysis p-adic numbers Distributionstheorie Wavelet Pseudodifferentialgleichung p-adische Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019014929&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000130 |
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