Advances in analysis, probability and mathematical physics: contributions of nonstandard analysis
In 1961 Robinson introduced an entirely new version of the theory of infinitesimals, which he named 'Nonstandard Analysis'. 'Nonstandard' here refers to the nature of new fields of numbers as defined by nonstandard models of the first-order theory of the reals. This system of num...
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Dordrecht u.a.
Kluwer
1995
|
| Series: | Mathematics and its applications
314 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | In 1961 Robinson introduced an entirely new version of the theory of infinitesimals, which he named 'Nonstandard Analysis'. 'Nonstandard' here refers to the nature of new fields of numbers as defined by nonstandard models of the first-order theory of the reals. This system of numbers was closely related to the ring of Schmieden and Laugwitz, developed independently a few years earlier. During the last thirty years the use of nonstandard models in mathematics has taken its rightful place among the various methods employed by mathematicians. The contributions in this volume have been selected to present a panoramic view of the various directions in which nonstandard analysis is advancing, thus serving as a source of inspiration for future research. Papers have been grouped in sections dealing with analysis, topology and topological groups; probability theory; and mathematical physics This volume can be used as a complementary text to courses in Nonstandard Analysis, and will be of interest to graduate students and researchers in both pure and applied mathematics and physics |
| Physical Description: | X, 251 S. |
| ISBN: | 0792331915 |
Staff View
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| 520 | 3 | |a In 1961 Robinson introduced an entirely new version of the theory of infinitesimals, which he named 'Nonstandard Analysis'. 'Nonstandard' here refers to the nature of new fields of numbers as defined by nonstandard models of the first-order theory of the reals. This system of numbers was closely related to the ring of Schmieden and Laugwitz, developed independently a few years earlier. During the last thirty years the use of nonstandard models in mathematics has taken its rightful place among the various methods employed by mathematicians. The contributions in this volume have been selected to present a panoramic view of the various directions in which nonstandard analysis is advancing, thus serving as a source of inspiration for future research. Papers have been grouped in sections dealing with analysis, topology and topological groups; probability theory; and mathematical physics | |
| 520 | |a This volume can be used as a complementary text to courses in Nonstandard Analysis, and will be of interest to graduate students and researchers in both pure and applied mathematics and physics | ||
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Record in the Search Index
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| adam_text | Table of Contents
Preface: vii
Part I: Analysis
S. Albeverio, D. Guido, A. Ponosov, S. Scarlatti: Singular traces and nonstandard
analysis 3
M. Capiriski, N. Cutland: Navier Stokes equations 20
E. I. Gordon: Hyperfinitt approximations of commutative topological groups .... 37
T. Norberg: A note on the myope topology 46
M. Oberguggenberger: Nonlinear theories of generalized functions 56
H. Osswald: A nonstandard approach to the Pettis integral 75
H. Ploss: A counterexample to the spectral mapping theorem revisited from a non
standard point of view 91
H. Render: Nonstandard polynominals in several variables 96
T. Todorov: An existence result for a class of partial differential equations with
smooth coefficients 107
B. Wietschorke: On the generation of topology by external equivalence relations 122
B. Zimmer: Nonstandard hulls of Lebesgue Bochner spaces 132
Part II: Probability Theory
H. Akiyama: A nonstandard approach to diffusions on manifolds and nonstandard
heat kernels 143
N.J. Cutland, Siu Ah Ng: A nonstandard approach to the Malliavin Calculus . 149
M. Kalina: Ergodic transformations in AST 171
D. Landers, L. Rogge: Nonstandard characterization for a general invariance prin¬
ciple 176
T. Lindstr0m: Andersons s Brownian motion and the infinite dimensional
Ornstein Uhlenbeck process 186
A. Ponosov: Two applications of NSA in the theory of stochastic dynamical
systems 200
D.A. Ross: Nonstandard methods and the space of experiments 212
Part III: Mathematical Physics
L. Arkeryd: Infinite range forces and strong L1 asymptotics for the space homoge¬
neous Boltzmann equation 221
M.P.H. Wolff: A nonstandard analysis approach to the theory of quantum meanfield
systems 228
Subject index 247
v
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| spelling | Advances in analysis, probability and mathematical physics contributions of nonstandard analysis ed. by Sergio A. Albeverio ... Dordrecht u.a. Kluwer 1995 X, 251 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 314 In 1961 Robinson introduced an entirely new version of the theory of infinitesimals, which he named 'Nonstandard Analysis'. 'Nonstandard' here refers to the nature of new fields of numbers as defined by nonstandard models of the first-order theory of the reals. This system of numbers was closely related to the ring of Schmieden and Laugwitz, developed independently a few years earlier. During the last thirty years the use of nonstandard models in mathematics has taken its rightful place among the various methods employed by mathematicians. The contributions in this volume have been selected to present a panoramic view of the various directions in which nonstandard analysis is advancing, thus serving as a source of inspiration for future research. Papers have been grouped in sections dealing with analysis, topology and topological groups; probability theory; and mathematical physics This volume can be used as a complementary text to courses in Nonstandard Analysis, and will be of interest to graduate students and researchers in both pure and applied mathematics and physics Analyse mathématique non standard - Congrès ram Nonstandard mathematical analysis Congresses Nonstandard-Analysis (DE-588)4137021-1 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1992 Blaubeuren gnd-content (DE-588)1071861417 Konferenzschrift 1992 Tübingen gnd-content Nonstandard-Analysis (DE-588)4137021-1 s DE-604 Albeverio, Sergio 1939- Sonstige (DE-588)121093999 oth Mathematics and its applications 314 (DE-604)BV008163334 314 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006719694&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Advances in analysis, probability and mathematical physics contributions of nonstandard analysis Mathematics and its applications Analyse mathématique non standard - Congrès ram Nonstandard mathematical analysis Congresses Nonstandard-Analysis (DE-588)4137021-1 gnd |
| subject_GND | (DE-588)4137021-1 (DE-588)1071861417 |
| title | Advances in analysis, probability and mathematical physics contributions of nonstandard analysis |
| title_auth | Advances in analysis, probability and mathematical physics contributions of nonstandard analysis |
| title_exact_search | Advances in analysis, probability and mathematical physics contributions of nonstandard analysis |
| title_full | Advances in analysis, probability and mathematical physics contributions of nonstandard analysis ed. by Sergio A. Albeverio ... |
| title_fullStr | Advances in analysis, probability and mathematical physics contributions of nonstandard analysis ed. by Sergio A. Albeverio ... |
| title_full_unstemmed | Advances in analysis, probability and mathematical physics contributions of nonstandard analysis ed. by Sergio A. Albeverio ... |
| title_short | Advances in analysis, probability and mathematical physics |
| title_sort | advances in analysis probability and mathematical physics contributions of nonstandard analysis |
| title_sub | contributions of nonstandard analysis |
| topic | Analyse mathématique non standard - Congrès ram Nonstandard mathematical analysis Congresses Nonstandard-Analysis (DE-588)4137021-1 gnd |
| topic_facet | Analyse mathématique non standard - Congrès Nonstandard mathematical analysis Congresses Nonstandard-Analysis Konferenzschrift 1992 Blaubeuren Konferenzschrift 1992 Tübingen |
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