P-adic valued distributions in mathematical physics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht u.a.
Kluwer Acad. Publ.
1994
|
| Series: | Mathematics and its applications
309 |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006649114&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | XVI, 264 S. |
| ISBN: | 0792331729 |
Staff View
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| 100 | 1 | |a Khrennikov, Andrei |d 1958- |e Verfasser |0 (DE-588)128568410 |4 aut | |
| 245 | 1 | 0 | |a P-adic valued distributions in mathematical physics |c by Andrei Khrennikov |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer Acad. Publ. |c 1994 | |
| 300 | |a XVI, 264 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Mathematics and its applications |v 309 | |
| 650 | 7 | |a Physique mathématique |2 ram | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 4 | |a p̲-adic analysis | |
| 650 | 0 | 7 | |a Mathematische Physik |0 (DE-588)4037952-8 |2 gnd |9 rswk-swf |
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Record in the Search Index
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|---|---|
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| _version_ | 1821931193959972865 |
| adam_text | Table of Contents
Introduction xi
I First Steps to Non Archimedean 1
1. Non Archimedean Number Fields 1
2. Ultrametrics 4
3. Fields of p adic Numbers 6
4. Extensions of Non Archimedean Fields 12
5. Normed and Locally Convex Spaces 17
6. Continuous, Differentiate and Analytic Functions . . 19
7. The Mahler Theory of an Integration on the Ring of
p adic Integers 24
II The Gauss, Lebesgue and Feynman Distributions
Over Non Archimedean Fields 31
1. Analytic Functions over Non Archimedean Fields . . 33
2. Analytic Distributions, Gauss and Feynman Distribu¬
tions in a Finite Dimensional Case 36
3. Non Archimedean Hilbert Space 43
4. The Space L2{Kn, e~lx dx) of Functions Square Summable
with Respect to the Canonical Gaussian Distribution 46
5. The Space L,2(Kn,dx) of Functions Square Summable
with Respect the Lebesgue Distribution 50
6. The Space Fi{Zn, 7) of Analytic Functions Square Summable
with Respect to the Canonical Complex Gaussian Dis¬
tribution 54
viii Table of Contents
7. Unboundedness of the p adic Gaussian Distribution . 55
8. The Volkenborn (Uniform) Distribution 64
III The Gauss and Feynman Distributions on Infinite
Dimensional Spaces over Non Archimedean Fields 65
1. Continuous Multilinear Forms 66
2. Generalized Functions on Infinite Dimensional Spaces 70
3. Laplace Transformation on Infinite Dimensional Spaces 76
4. Linear Partial Differential Equations on Infinite Dimensional
Spaces 79
IV Quantum Mechanics for Non Archimedean Wave
Functions 85
1. Schrodinger and Bargmann Fock Representations in
Non Archimedean Quantum Mechanics 87
2. Non Archimedean Quantum Statistical Mechanics . . 92
3. The Theorems of the Existence and Uniqueness of So¬
lution of Linear Partial Differential Equations on Non
Archimedean Spaces 93
4. Solvability of the Schrodinger, Heisenberg and Liou
ville Equations in Non Archimedean Mechanics ... 95
5. Two Measurement Processes: a Scale with an Infinite
Decrease of 1 and a Scale with an Infinite Increase of
1 96
6. Non Archimedean Cosmology 98
7. Microcosm and the Non Archimedean Structure of the
Real Minkowski Space Time 100
8. Models with an Infinitely Large Number of Particles 102
9. The p adic Interpretation of Tachyons 104
V Functional Integrals and the Quantization of Non
Archimedean Models with an Infinite Number of
Degrees of Freedom 107
1. Lagrange s Formalism for a Non Archimedean Scalar
Boson Field 107
Table of Contents ix
2. The Gauss and Feynman Integrals for a Non Archimedean
Quantum Scalar Boson Field Ill
3. The Bargmann Fock Representation 113
VI The p Adic Valued Probability Measures 115
1. p Adic Frequency Theory of Probability 116
2. Axiomatics on the Basis of Finite Additive Measures 119
3. Monna Springer Theory of Integration with Respect to
Non Archimedean Valued Measures 123
4. Measures Decreasing on the Infinity 127
5. The Product of a Function and a Measure 129
6. A Formula of an Exchange of Variables in the Inte¬
gral of Monna Springer with Respect to the Decreasing
Measure 130
7. p adic Valued Probability Measures 134
8. Bernoulli p adic Valued Probabilities on the Ring of
the q adic Integers 147
9. Biological Models Connected with the p adic Valued
Bernoulli Distributions 150
10. A Limit Theorem for Sums of Independent Random
Variables 153
11. Discrete Probabilities. A p adic Interpretation of St. Pe¬
tersburg Paradox 155
VII Statistical Stabilization with Respect to p adic and
Real Metrics 161
1. p Adic Statistical Simulation 162
2. On a Definition of the p adic Frequency Probability . 171
3. What Can We Do with p adic Probabilities? 177
4. The First Step to the p adic Theory of Information . 179
5. A Probability Model of a p adic Coin 180
6. On the Kolmogorov Complexity of p adic Random Se¬
quences 186
7. The Statistical Interpretation of Quantum Models with
Wave Functions Assuming Values in the Quadratic Ex¬
tensions of the Field of p adic Numbers 190
x Table of Contents
VIII The p adic Valued Probability Distributions (Gen¬
eralized Functions) 193
1. Axiomatics 193
2. Probability Distributions on Spaces of p adic Sequences 197
3. A Limit Theorem 203
4. Convergence of Series of Independent Random Vari¬
ables 205
5. The p adic White Noise. An Analogue of Hida s Cal¬
culus 207
IX p Adic Superanalysis 215
1. Infinitely Generated p adic Banach Superalgebras . . 217
2. Spectral Properties 220
3. Differential Calculus on the p adic Banach Superspace 225
4. p Adic Supermanifolds 231
Bibliographical Remarks 235
Open Problems 239
Appendix 241
1. Expansion of Numbers in a Given Scale 241
2. An Analogue of Newton s Method 244
3. Non Existence of Differential Maps from Qp to M . . 246
Bibliography 249
Index 263
|
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| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV010027303 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T09:46:33Z |
| institution | BVB |
| isbn | 0792331729 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006649114 |
| oclc_num | 31167100 |
| open_access_boolean | |
| owner | DE-12 DE-384 DE-188 DE-91G DE-BY-TUM |
| owner_facet | DE-12 DE-384 DE-188 DE-91G DE-BY-TUM |
| physical | XVI, 264 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spellingShingle | Khrennikov, Andrei 1958- P-adic valued distributions in mathematical physics Mathematics and its applications Physique mathématique ram Mathematische Physik Mathematical physics p̲-adic analysis Mathematische Physik (DE-588)4037952-8 gnd p-adische Analysis (DE-588)4252360-6 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4252360-6 |
| title | P-adic valued distributions in mathematical physics |
| title_auth | P-adic valued distributions in mathematical physics |
| title_exact_search | P-adic valued distributions in mathematical physics |
| title_full | P-adic valued distributions in mathematical physics by Andrei Khrennikov |
| title_fullStr | P-adic valued distributions in mathematical physics by Andrei Khrennikov |
| title_full_unstemmed | P-adic valued distributions in mathematical physics by Andrei Khrennikov |
| title_short | P-adic valued distributions in mathematical physics |
| title_sort | p adic valued distributions in mathematical physics |
| topic | Physique mathématique ram Mathematische Physik Mathematical physics p̲-adic analysis Mathematische Physik (DE-588)4037952-8 gnd p-adische Analysis (DE-588)4252360-6 gnd |
| topic_facet | Physique mathématique Mathematische Physik Mathematical physics p̲-adic analysis p-adische Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006649114&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT khrennikovandrei padicvalueddistributionsinmathematicalphysics |
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