Potential theory in Euclidean spaces:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Tokyo
Gakkōtosho
1996
|
| Schriftenreihe: | [GAKUTO international series / Mathematical sciences and applications]
6 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 341 S. |
| ISBN: | 4762504157 |
Internformat
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Datensatz im Suchindex
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| adam_text | GAKUTO INTERNATIONAL SERIES MATHEMATICAL SCIENCES AND APPLICATIONS
VOLUME 6 POTENTIAL THEORY IN EUCLIDEAN SPACES YOSHIHIRO MIZUTA THE
DIVISION OF MATHEMATICAL AND INFORMATION SCIENCES FACULTY OF INTEGRATED
ARTS AND SCIENCES HIROSHIMA UNIVERSITY HIGASHI-HIROSHIMA 724, JAPAN
JANUARY 1996 GAKKOTOSHO, TOKYO, JAPAN CONTENTS PREFACE I CONTENTS III
NOTATION VI 1 MEASURE THEORY 1 1.1 MEASURES X 1 1.2 BOREL SETS 4 1.3
SUSLIN SETS 7 1.4 MEASURABLE FUNCTIONS 12 1.5 LEBESGUE INTEGRAL 17 1.6
LINEAR FUNCTIONALS 21 1.7 RIEMANN-STIELTJES INTEGRAL 27 1.8 PRODUCT
MEASURES 30 1.9 HAUSDORFF MEASURES 33 1.10 MAXIMAL FUNCTIONS 37 1.11
DISTRIBUTIONS 44 1.12 L P -SPACES 48 2 POTENTIALS OF MEASURES 55 2.1
RIESZ POTENTIALS 55 2.2 FOURIER TRANSFORM 61 2.3 MINIMAX LEMMA 68 2.4
CAPACITY 71 2.5 FINE LIMITS 77 2.6 LOGARITHMIC POTENTIALS 81 2.7
RELATIONSHIP BETWEEN HAUSDORFF MEASURES AND CAPACITIES 86 2.8 RADIAL
LIMITS 91 2.9 ENERGY INTEGRAL . - 94 2.10 GAUSS VARIATION 97 IN IV
CONTENTS 3 HARMONIC FUNCTIONS 104 3.1 HARMONIC FUNCTIONS 104 3.2
SUPERHARMONIC FUNCTIONS ILL 3.3 BOUNDARY LIMITS OF SUPERHARMONIC
FUNCTIONS 119 3.4 KELVIN TRANSFORM 127 3.5 BALAYAGE 130 3.6 THE
CLASSICAL DIRICHLET PROBLEM 135 3.7 DIRICHLET PROBLEM IN THE PLANE ,.
138 3.8 REMOVABLE SINGULARITIES 140 4 RIESZ POTENTIALS OF FUNCTIONS IN
IP 147 4.1 THE MARCINKIEWICZ INTERPOLATION THEOREM 147 4.2 SOBOLEV S
INEQUALITY 153 4.3 SPHERICAL MEANS IN X 9 157 4.4 RESTRICTION PROPERTY
160 4.5 INVERSE PROPERTY 162 5 CONTINUITY PROPERTIES OF POTENTIALS OF
FUNCTIONS IN L P 166 5.1 (&,P)-CAPACITY 166 5.2 RELATIONS AMONG (A,
P)-CAPACITIES 174 5.3 CONTINUITY PROPERTIES 177 5.4 FINE LIMITS 181 5.5
CONTRACTIVE PROPERTY OF (A, P)-CAPACITIES 186 5.6 RADIAL LIMITS 189 /
5.7 FINE DIFFERENTIABILITY 192 5.8 DIFFERENTIABILITY 198 5.9 LOGARITHMIC
POTENTIALS 204 6 BEPPO LEVI FUNCTIONS 205 6.1 SOBOLEV S INTEGRAL
REPRESENTATION 205 6.2 CANONICAL REPRESENTATION 208 6.3 THEORY OF
SINGULAR INTEGRALS 210 6.4 APPLICATIONS OF SINGULAR INTEGRAL THEORY 220
6.5 PARTIAL DIFFERENTIABUITY 224 6.6 BEPPO LEVI SPACES 227 6.7
CONTINUITY PROPERTIES OF BLD FUNCTIONS 233 6.8 DIRICHLET SPACE 235 7
BESSEL POTENTIALS 245 7.1 BESSEL KERNEL 245 7.2 BESSEL POTENTIALS 247
7.3 BESSEL CAPACITY 251 7.4 POISSON KERNEL IN THE HALF SPACE 253 7.5 THE
LIPSCHITZ SPACES A* 260 CONTENTS V 7.6 THE RELATIONSHIPS BETWEEN L PA
AND A* 270 7.7 RESTRICTION AND EXTENSION OF BESSEL POTENTIALS 274 8
BOUNDARY LIMITS 281 8.1 BOUNDARY LIMITS FOR GREEN POTENTIALS 281 8.2
BOUNDARY LIMITS FOR BLD FUNCTIONS 296 8.3 NONTANGENTIAL AND TANGENTIAL
LIMITS 311 8.4 POLYHARMONIC FUNCTIONS 315 8.5 MONOTONE FUNCTIONS 325
INDEX 329 GENERAL REFERENCES 333 BIBLIOGRAPHY 335
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:15:29Z |
| institution | BVB |
| isbn | 4762504157 |
| language | English |
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| physical | VIII, 341 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Gakkōtosho |
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| series2 | [GAKUTO international series / Mathematical sciences and applications] |
| spelling | Mizuta, Yoshihiro Verfasser aut Potential theory in Euclidean spaces Yoshihiro Mizuta Tokyo Gakkōtosho 1996 VIII, 341 S. txt rdacontent n rdamedia nc rdacarrier [GAKUTO international series / Mathematical sciences and applications] 6 Green's functions Harmonic functions Potential theory (Mathematics) Potenzialtheorie (DE-588)4046939-6 gnd rswk-swf Euklidischer Raum (DE-588)4309127-1 gnd rswk-swf Potenzialtheorie (DE-588)4046939-6 s Euklidischer Raum (DE-588)4309127-1 s DE-604 Mathematical sciences and applications] [GAKUTO international series 6 (DE-604)BV011762304 6 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007943893&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mizuta, Yoshihiro Potential theory in Euclidean spaces Green's functions Harmonic functions Potential theory (Mathematics) Potenzialtheorie (DE-588)4046939-6 gnd Euklidischer Raum (DE-588)4309127-1 gnd |
| subject_GND | (DE-588)4046939-6 (DE-588)4309127-1 |
| title | Potential theory in Euclidean spaces |
| title_auth | Potential theory in Euclidean spaces |
| title_exact_search | Potential theory in Euclidean spaces |
| title_full | Potential theory in Euclidean spaces Yoshihiro Mizuta |
| title_fullStr | Potential theory in Euclidean spaces Yoshihiro Mizuta |
| title_full_unstemmed | Potential theory in Euclidean spaces Yoshihiro Mizuta |
| title_short | Potential theory in Euclidean spaces |
| title_sort | potential theory in euclidean spaces |
| topic | Green's functions Harmonic functions Potential theory (Mathematics) Potenzialtheorie (DE-588)4046939-6 gnd Euklidischer Raum (DE-588)4309127-1 gnd |
| topic_facet | Green's functions Harmonic functions Potential theory (Mathematics) Potenzialtheorie Euklidischer Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007943893&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011762304 |
| work_keys_str_mv | AT mizutayoshihiro potentialtheoryineuclideanspaces |