Logarithmic potentials with external fields:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1997
|
| Series: | Grundlehren der mathematischen Wissenschaften
316 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 505 S. |
| ISBN: | 3540570780 |
Staff View
MARC
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| 245 | 1 | 0 | |a Logarithmic potentials with external fields |c Edward B. Saff ; Vilmos Totik |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1997 | |
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Record in the Search Index
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| adam_text | Table of Contents
Chapter 0. Preliminaries 1
0.1 Weak* Topology and Lower Semi continuity 1
0.2 Fundamentals of Harmonic Functions 6
0.3 Series Representations of Harmonic Functions 9
0.4 Poisson s Formula and Applications 12
0.5 Superharmonic Functions 18
Chapter I. Weighted Potentials 23
1.1 The Energy Problem 24
1.2 Minimum Principle, Dirichlet Problem 35
1.3 The Extremal Measure 43
1.4 The Equilibrium Potential 49
1.5 Fine Topology and Continuity of Equilibrium Potentials 58
1.6 Weighted Capacity 63
1.7 Notes and Historical References 74
Chapter II. Recovery of Measures, Green Functions and Balayage 81
II. 1 Recovering a Measure from Its Potential 83
11.2 The Unicity Theorem 97
11.3 Riesz Decomposition Theorem and Principle of Domination 100
11.4 Green Functions and Balayage Measures 108
11.5 Green Potentials 123
11.6 Notes and Historical References 137
Chapter III. Weighted Polynomials 141
III. 1 Weighted Fekete Points, Transfinite Diameter
and Fekete Polynomials 142
111.2 Where Does the Sup Norm of a Weighted Polynomial Live? 153
111.3 Weighted Chebyshev Polynomials 162
111.4 Zero Distribution of Polynomials of Asymptotically
Minimal Weighted Norm 169
XIV Table of Contents
111.5 The Function of Leja and Siciak 177
111.6 Where Does the Lp Norm of a Weighted Polynomial Live? 180
111.7 Notes and Historical References 187
Chapter IV. Determination of the Extremal Measure 191
IV. 1 The Support Sw of the Extremal Measure 192
IV.2 The Fourier Method and Smoothness Properties
of the Extremal Measure jxw 209
IV.3 The Integral Equation 221
IV.4 Behavior of /jlwx 227
IV.5 Exponential and Power Type Functions 238
IV.6 Circular Symmetric Weights 245
IV.7 Some Problems from Physics 246
IV.7.1 Contact Problem of Elasticity 246
IV.7.2 Distribution of Energy Levels of Quantum Systems 249
IV.7.3 An Electrostatic Problem for an Infinite Wire 251
IV.8 Notes and Historical References 254
Chapter V. Extremal Point Methods 257
V.I Leja Points and Numerical Determination of fiw 257
V.2 The Extremal Point Method for Solving Dirichlet Problems 267
V.3 The Extremal Point Method for Determining Green Functions
and Conformal Mappings 273
V.4 Notes and Historical References 275
Chapter VI. Weights on the Real Line 277
VI. 1 The Approximation Problem 278
VI.2 Approximation with Varying Weights 301
VI.3 Fast Decreasing Polynomials 313
VI.4 Discretizing a Logarithmic Potential 326
VI.5 Norm Inequalities for Weighted Polynomials
with Exponential Weights 334
VI.6 Comparisons of Different Weighted Norms of Polynomials 343
VI.7 n Widths for Weighted Entire Functions 349
VI.8 Notes and Historical References 352
Chapter VII. Applications Concerning Orthogonal Polynomials 359
VII. 1 Zero Distribution and n th Root Asymptotics
for Orthogonal Polynomials with Exponential Weights 359
VII.2 Strong Asymptotics 364
VII.3 Weak* Limits of Zeros of Orthogonal Polynomials 373
VII.4 Notes and Historical References 379
Table of Contents XV
Chapter VIII. Signed Measures 381
VIII. 1 The Energy Problem for Signed Measures 382
VIII.2 Basic Theorems for Equilibrium Potentials and Measures
Associated with Signed Measures 388
VIII.3 Rational Fekete Points and a Weighted Variant
of a Problem of Zolotarjov 394
VIII.4 Examples 403
VIII.5 Rational Approximation of Signum Type Functions 409
VIII.6 Conformal Mapping of Ring Domains 421
VIII.7 A Discrepancy Theorem for Simple Zeros of Polynomials 426
VIII.8 Notes and Historical References 442
Appendix A. The Dirichlet Problem and Harmonic Measures 449
A. 1 Regularity with Respect to Green Functions 449
A.2 Regularity with Respect to Dirichlet Problems 454
A.3 Harmonic Measures and the Generalized Poisson Formula 458
Appendix B. Weighted Approximation in CN 465
B. 1 Pluripotential Theory 466
B.2 Weighted Polynomials in CN 471
B.3 Fekete Points 478
B.4 Notes and Historical References 480
Basic Results of Potential Theory 483
Bibliography 485
List of Symbols 495
Index 501
|
| any_adam_object | 1 |
| author | Saff, Edward B. 1944- Totik, Vilmos 1954- |
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| author_facet | Saff, Edward B. 1944- Totik, Vilmos 1954- |
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| callnumber-first | Q - Science |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 560 SK 820 SK 890 |
| ctrlnum | (OCoLC)246632423 (DE-599)BVBBV011497450 |
| dewey-full | 515.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.9 |
| dewey-search | 515.9 |
| dewey-sort | 3515.9 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011497450 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:10:47Z |
| institution | BVB |
| isbn | 3540570780 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007737482 |
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| physical | XV, 505 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer |
| record_format | marc |
| series | Grundlehren der mathematischen Wissenschaften |
| series2 | Grundlehren der mathematischen Wissenschaften |
| spelling | Saff, Edward B. 1944- Verfasser (DE-588)110736990 aut Logarithmic potentials with external fields Edward B. Saff ; Vilmos Totik Berlin [u.a.] Springer 1997 XV, 505 S. txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften 316 Potential theory (Mathematics) Potenzialtheorie (DE-588)4046939-6 gnd rswk-swf Logarithmisches Potenzial (DE-588)4168046-7 gnd rswk-swf Potenzialtheorie (DE-588)4046939-6 s DE-604 Logarithmisches Potenzial (DE-588)4168046-7 s Totik, Vilmos 1954- Verfasser (DE-588)111480485 aut Grundlehren der mathematischen Wissenschaften 316 (DE-604)BV000000395 316 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007737482&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Saff, Edward B. 1944- Totik, Vilmos 1954- Logarithmic potentials with external fields Grundlehren der mathematischen Wissenschaften Potential theory (Mathematics) Potenzialtheorie (DE-588)4046939-6 gnd Logarithmisches Potenzial (DE-588)4168046-7 gnd |
| subject_GND | (DE-588)4046939-6 (DE-588)4168046-7 |
| title | Logarithmic potentials with external fields |
| title_auth | Logarithmic potentials with external fields |
| title_exact_search | Logarithmic potentials with external fields |
| title_full | Logarithmic potentials with external fields Edward B. Saff ; Vilmos Totik |
| title_fullStr | Logarithmic potentials with external fields Edward B. Saff ; Vilmos Totik |
| title_full_unstemmed | Logarithmic potentials with external fields Edward B. Saff ; Vilmos Totik |
| title_short | Logarithmic potentials with external fields |
| title_sort | logarithmic potentials with external fields |
| topic | Potential theory (Mathematics) Potenzialtheorie (DE-588)4046939-6 gnd Logarithmisches Potenzial (DE-588)4168046-7 gnd |
| topic_facet | Potential theory (Mathematics) Potenzialtheorie Logarithmisches Potenzial |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007737482&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000395 |
| work_keys_str_mv | AT saffedwardb logarithmicpotentialswithexternalfields AT totikvilmos logarithmicpotentialswithexternalfields |