Potential theory in modern function theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Chelsea Publ. Co.
1975
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 590 S. Ill. |
| ISBN: | 0828402817 |
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MARC
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| 245 | 1 | 0 | |a Potential theory in modern function theory |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York, NY |b Chelsea Publ. Co. |c 1975 | |
| 300 | |a X, 590 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Application conforme | |
| 650 | 4 | |a Fonctions harmoniques | |
| 650 | 7 | |a Matematica |2 larpcal | |
| 650 | 4 | |a Potentiel, Théorie du | |
| 650 | 4 | |a Conformal mapping | |
| 650 | 4 | |a Harmonic functions | |
| 650 | 4 | |a Potential theory (Mathematics) | |
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Record in the Search Index
| _version_ | 1804116409594150912 |
|---|---|
| adam_text | CONTENTS
CHAPTER I. DIRICHLET PROBLEM
1. Subharmonic and superharmonic functions 1
2. Upper and lower functions 3
3. Dirichlet problem 4
4. Regular and irregular points 6
5. Dirichlet principle 9
6. Green s function 14
7. Selberg s theorem on Green s function 22
8. Neumann s problem 27
9. Mixed boundary value problem 31
CHAPTER n. SUBHARMONIC FUNCTIONS
1. Caratheodory s outer measure 33
2. Selection theorem 34
3. Semi continuous function 35
4. Subharmonic function 37
5. Approximation theorem 43
6. Logarithmic potential 45
7. Some lemmas 46
8. F. Riesz decomposition theorem 48
CHAPTER III. POTENTIAL THEORY
1. Maximum principle for logarithmic potential 53
2. Capacity. Conductor potential 54
3. Fundamental theorem 60
4. Hausdorff s measure 63
5. Transfinite diameter. Tchebycheff s constant 71
6. Evans theorem 75
7. Maximum principle for harmonic function 77
8. Kellogg s theorem 80
9. Mapping radius 84
VI Contents
10. Balayage 86
11. Elliptic capacity 89
12. Hyperbolic capacity 94
13. Modulus of a ring domain 96
14. Capacity potential 100
15. Criteria of regularity 104
16. General Cantor set 106
17. Harmonic measure Ill
18. Dirichlet problem with unbounded boundary values 118
19. Wiman s theorem 120
20. Capacity of a set in the space of regular functions 123
CHAPTER IV. POISSON INTEGRAL
1. Poisson integral 129
2. Fatou s theorem 135
3. Remark on Fatou s theorem 137
4. Poisson integral of two variables 139
5. Positive harmonic function in a unit circle 143
6. Positive harmonic function in a half plane 149
7. Caratheodory Toeplitz s theorem 153
8. I. Schur s theorem 159
9. Conjugate function 161
10. Littlewood s theorem on subharmonic functions in | z | 1 169
11. Hardy Littlewood s maximal theorem 180
12. Non negative subharmonic function in a half plane 188
CHAPTER V. NEVANLINNA S THEORY OF
MEROMORPHIC FUNCTIONS
1. First fundamental theorem 195
2. On m(r, a) 199
3. Function of bounded type 202
4. Order of a meromorphic function 203
5. Second fundamental theorem 205
6. On mf — ,r, =°) 213
7. Theorems of Picard type 214
Contents VII
8. Canonical product for a meromorphic function for z oo 216
9. Order of the derivative of a meromorphic function for |z| oo 220
10. Canonical product for a meromorphic function in z 1 221
11. Order of the derivative of a meromorphic function in z 1 227
12. Direct transcendental singularity 232
13. Meromorphic function in a neighbourhood of a closed set of capacity zero .. 237
CHAPTER VI. AHLFORS THEORY OF
COVERING SURFACES
1. Constants d0, h0, do(/3), A0(j3) 243
2. Ahlfors covering theorem 243
3. Ahlfors fundamental theorem 246
4. Simply connected finite covering surfaces of a sphere 252
5. Regular exhaustion in Ahlfors sense 256
6. Bloch s theorem and related theorems 259
7. A criterion on normal family 262
8. Uniformization of algebraic functions 264
9. Schottky s theorem and related theorems 266
CHAPTER VII. BOREL S DIRECTION
1. Borel s theorem 271
PART I. Meromorphic functions for |z| °°
1. Analogue of the second fundamental theorem for an angular domain 272
2. Borel s direction 273
3. A lemma 277
4. Biernacki Rauch s theorem 282
5. Meromorphic function in an angular domain 284
PART II. Meromorphic functions in |z| l
1. Analogue of the second fundamental theorem for an angular domain 288
2. A lemma 291
3. Analogue of Biernacki Rauch s theorem 293
4. Function of the class Hm T{f, r)/log = i = ~ 297
5. Function of the class Hm T(J, r)==° 299
VIII Contents
CHAPTER VIII. CLUSTER SET OF
A MEROMORPHIC FUNCTION
1. Principle of majoration by harmonic measure 301
2. Converse of Abel s theorem 308
3. Function of H^ class 314
4. F. and M. Riesz theorem on conformal mapping 318
5. Lusin Privaloff s theorem 320
6. Extension of Lowner s theorem 322
7. Function of !7 class 323
8. Implicit function y(x), defined by an integral relation G(x, j/)=0 329
9. Cluster set of a meromorphic function at a non isolated boundary point .. 331
10. Cluster set of a meromorphic function in z 1 337
11. Fejer and F. Riesz s theorem and its extension by M. Riesz 339
12. Functions of class (D) and (£ *) 343
CHAPTER IX. CONFORMAL MAPPING
PART I. Simply connected domains
1. Theorems of Caratteodory and Lindelof 352
2. Theorems of Fejer and Lindelof 356
3. Kellogg s theorem 359
4. Angular derivative 365
5. Fundamental lemma 368
6. Proof of Theorem IX. 9 374
7. Remark on Theorem IX. 9 377
8. Variable domains 381
9. Lowner s differential equation 387
10. Rengel s inequality 393
PART II. Multiply connected domains
1. Conformal mapping on a parallel slits plane 396
2. Conformal mapping on a circular, or a radial slits plane 403
3. Conformal mapping on a circular, or a radial slits disc 408
4. Conformal mapping on a circular, or a radial slits ring 413
5. Conformal mapping on an Ti sheeted circular disc 417
Contents IX
6. Conformal mapping of an open Riemann surface of planar character on a
schlicht domain 421
7. Conformal mapping on a circular domain 424
8. Moduli of plane regions 426
CHAPTER X. RIEMANN SURFACE
1. Classification of open Riemann surfaces 429
2. Harmonic measure of the ideal boundary of an open Riemann surface.... 430
3. Open Riemann surfaces of class Oo and Pa 433
4. Theorems of Bader Parreau and Virtanen 442
5. Open Riemann surfaces of class Oad 445
6. Open Riemann surfaces of class Omd and Pud* 447
7. Modified Green s function 449
8. Potential function with two logarithmic singularities 456
9. Abelian integral of the first kind 460
10. Potential function with a polar singularity 464
11. Reciprocal relations 467
12. Riemann Roch s theorem 471
13. Royden s theorem 476
14. Schottkyan covering surfaces of a closed Riemann surface 478
15. Abelian covering surfaces of a closed Riemann surface 481
16. Conformal mappings of a Riemann surface on itself 496
17. Moduli of closed Riemann surfaces of genus p S1 501
18. Prolongation of a Riemann surface 504
CHAPTER XI. FUCHSIAN GROUP
1. Non euclidean metric in |z| 1 509
2. Fundamental domain 512
3. Type of Fuchsian groups 514
4. Riemann surface Fa 519
5. Green s function of Fa 522
6. Ideal boundary of Fo 530
7. Hopf s ergodic theorem 535
8. Myrberg s approximation theorem 542
9. Analogue of Weyl s theorem on uniform distribution 544
X Contents
10. Fundamental Theorem 549
11. Some consequences from the Fundamental Theorem 554
12. Geometry of numbers for Fuchsian groups 559
13. Lattice points in a circle
APPENDIX
Birkhoff s ergodic theorem
BIBLIOGRAPHY 577
LIST OF AUTHORS 587
INDEX 589
|
| any_adam_object | 1 |
| author | Tsuji, Matasugu |
| author_facet | Tsuji, Matasugu |
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| author_sort | Tsuji, Matasugu |
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| classification_rvk | SK 750 |
| ctrlnum | (OCoLC)858726 (DE-599)BVBBV001966185 |
| dewey-full | 515/.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.7 |
| dewey-search | 515/.7 |
| dewey-sort | 3515 17 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV001966185 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:38:03Z |
| institution | BVB |
| isbn | 0828402817 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001282271 |
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| physical | X, 590 S. Ill. |
| publishDate | 1975 |
| publishDateSearch | 1975 |
| publishDateSort | 1975 |
| publisher | Chelsea Publ. Co. |
| record_format | marc |
| spelling | Tsuji, Matasugu Verfasser aut Potential theory in modern function theory 2. ed. New York, NY Chelsea Publ. Co. 1975 X, 590 S. Ill. txt rdacontent n rdamedia nc rdacarrier Application conforme Fonctions harmoniques Matematica larpcal Potentiel, Théorie du Conformal mapping Harmonic functions Potential theory (Mathematics) Potenzialtheorie (DE-588)4046939-6 gnd rswk-swf Harmonische Funktion (DE-588)4159122-7 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Potenzialtheorie (DE-588)4046939-6 s Harmonische Funktion (DE-588)4159122-7 s DE-604 Funktionentheorie (DE-588)4018935-1 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001282271&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tsuji, Matasugu Potential theory in modern function theory Application conforme Fonctions harmoniques Matematica larpcal Potentiel, Théorie du Conformal mapping Harmonic functions Potential theory (Mathematics) Potenzialtheorie (DE-588)4046939-6 gnd Harmonische Funktion (DE-588)4159122-7 gnd Funktionentheorie (DE-588)4018935-1 gnd |
| subject_GND | (DE-588)4046939-6 (DE-588)4159122-7 (DE-588)4018935-1 |
| title | Potential theory in modern function theory |
| title_auth | Potential theory in modern function theory |
| title_exact_search | Potential theory in modern function theory |
| title_full | Potential theory in modern function theory |
| title_fullStr | Potential theory in modern function theory |
| title_full_unstemmed | Potential theory in modern function theory |
| title_short | Potential theory in modern function theory |
| title_sort | potential theory in modern function theory |
| topic | Application conforme Fonctions harmoniques Matematica larpcal Potentiel, Théorie du Conformal mapping Harmonic functions Potential theory (Mathematics) Potenzialtheorie (DE-588)4046939-6 gnd Harmonische Funktion (DE-588)4159122-7 gnd Funktionentheorie (DE-588)4018935-1 gnd |
| topic_facet | Application conforme Fonctions harmoniques Matematica Potentiel, Théorie du Conformal mapping Harmonic functions Potential theory (Mathematics) Potenzialtheorie Harmonische Funktion Funktionentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001282271&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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