Riemann's boundary problem with infinite index:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
Basel ; Boston, Mass. ; Berlin
Birkhäuser Verlag
1994
|
| Schriftenreihe: | Operator Theory
67 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Russischen übersetzt |
| Beschreibung: | XI, 252 Seiten graph. Darst. |
| ISBN: | 3764329998 0817629998 |
Internformat
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| 100 | 1 | |a Govorov, Nikolaj V. |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Kraevaja zadača Rimana s bezkonečnym indeksom |
| 245 | 1 | 0 | |a Riemann's boundary problem with infinite index |c N. V. Govorov |
| 264 | 1 | |a Basel ; Boston, Mass. ; Berlin |b Birkhäuser Verlag |c 1994 | |
| 300 | |a XI, 252 Seiten |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Operator Theory |v 67 | |
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| 650 | 7 | |a Problèmes aux limites |2 ram | |
| 650 | 7 | |a Riemann, surfaces de |2 ram | |
| 650 | 7 | |a Riemann-Hilbert, problèmes de |2 ram | |
| 650 | 7 | |a problème Riemann |2 inriac | |
| 650 | 7 | |a problème aux limites |2 inriac | |
| 650 | 4 | |a Boundary value problems | |
| 650 | 4 | |a Index theory (Mathematics) | |
| 650 | 4 | |a Riemann surfaces | |
| 650 | 4 | |a Riemann-Hilbert problems | |
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Datensatz im Suchindex
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| adam_text |
CONTENTS
INTRODUCTION vii
PREFACE ix
PART I 1
GENERAL PROPERTIES OF ANALYTIC AND FINITE ORDER
FUNCTIONS IN THE HALF PLANE 1
1 Definition of order and indicator of a function holomorphic
in an angle. Relations between various definitions of order . 1
2 Generalized Nevanlinna and Carleman formulas 15
3 Canonical representation of a function of finite order in the
half plane 23
NECESSARY CONDITIONS OF COMPLETELY REGULAR
GROWTH IN THE HALF PLANE 38
4 Definition of completely regular growth in the half plane.
List of results on completely regular growth 38
5 Relation between completely regular growth in open and
closed angles 44
6 Asymptotic behavior of the modulus and zero distributions
of entire functions of the class A*p 53
7 Existence of argument boundary density for the zero set of
a function from the class A* 64
8 Existence of boundary and argument densities for the zero
set of a function from A*p 71
SUFFICIENT CONDITIONS OF COMPLETELY REGULAR
GROWTH IN THE HALF PLANE AND FORMULAS FOR
INDICATORS 76
9 The growth of some auxiliary functions of non integer order 76
10 A criterion for a function to belong to the class A* p being
non integer 81
11 A criterion for a function to belong to the class A*p, p being
non integer 87
12 The argument boundary symmetry of the zero set of a func¬
tion of the class A*p, p being integer 90
13 The growth of some auxiliary functions of integer order . . 94
14 A criterion for a function to belong to the class A* p integer 100
15 A criterion for a function to belong to the class A* p integer 105
16 Functions of the class A*p for even and for odd p 107
17 Functions of a finite degree in the half plane 112
vi CONTENTS
PART II 116
RIEMANN BOUNDARY PROBLEM WITH AN INFINITE INDEX
WHEN THE VERTICITY INDEX IS LESS THAN 1/2 . . 116
18 Statement of the homogeneous problem 116
19 Canonical function 118
20 Solution of the homogeneous problem in the class Bl De¬
scription of solutions of order p 124
21 Formulation of the non homogeneous problem and an ap¬
proach to its solution 128
22 Solution of the non homogeneous problem 132
RIEMANN BOUNDARY PROBLEM WITH INFINITE INDEX IN
THE CASE OF VERTICITY OF INFINITE ORDER . 137
23 Statement of the homogeneous problem 137
24 Canonical function 139
25 Asymptotic properties of zero sets of solutions of the homo¬
geneous problem from the classes B and _B* 142
26 General form of solutions of the homogeneous problem in the
class B 157
27 General form of solutions of the homogeneous problem in the
class B* 166
28 An example of a solution of the homogeneous problem in the
class Ba. Importance of the restriction on the exponent in
the Holder condition for the function tp(t) = a,rgG(t)/(2Trtp) 175
29 Statement of the non homogeneous problem and an approach
to its solution 184
30 Auxiliary statements 187
31 Solution of the homogeneous problem 200
RIEMANN BOUNDARY PROBLEM WITH A NEGATIVE INDEX 204
32 An example of a solvable homogeneous problem with a neg¬
ative index 204
33 Conditions of unsolvability of the homogeneous problem with
a negative index 211
34 Conditions of solvability of the non homogeneous problem
with an index —oo 223
ON THE PALEY PROBLEM 232
A.I Formulation of the problem and proof of the main inequality 232
A.2 Solution of the Paley problem 243
BIBLIOGRAPHY 249 |
| any_adam_object | 1 |
| author | Govorov, Nikolaj V. |
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| illustrated | Illustrated |
| indexdate | 2024-08-20T00:34:35Z |
| institution | BVB |
| isbn | 3764329998 0817629998 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005843579 |
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| physical | XI, 252 Seiten graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Birkhäuser Verlag |
| record_format | marc |
| series | Operator Theory |
| series2 | Operator Theory |
| spelling | Govorov, Nikolaj V. Verfasser aut Kraevaja zadača Rimana s bezkonečnym indeksom Riemann's boundary problem with infinite index N. V. Govorov Basel ; Boston, Mass. ; Berlin Birkhäuser Verlag 1994 XI, 252 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Operator Theory 67 Aus dem Russischen übersetzt Functionaalanalyse gtt Index, théorie de l' (Mathématiques) ram Problèmes aux limites ram Riemann, surfaces de ram Riemann-Hilbert, problèmes de ram problème Riemann inriac problème aux limites inriac Boundary value problems Index theory (Mathematics) Riemann surfaces Riemann-Hilbert problems Analytische Funktion (DE-588)4142348-3 gnd rswk-swf Asymptotische Entwicklung (DE-588)4112609-9 gnd rswk-swf Riemannsches Randwertproblem (DE-588)4317184-9 gnd rswk-swf Analytische Funktion (DE-588)4142348-3 s Asymptotische Entwicklung (DE-588)4112609-9 s DE-604 Riemannsches Randwertproblem (DE-588)4317184-9 s Operator Theory 67 (DE-604)BV000000970 67 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005843579&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Govorov, Nikolaj V. Riemann's boundary problem with infinite index Operator Theory Functionaalanalyse gtt Index, théorie de l' (Mathématiques) ram Problèmes aux limites ram Riemann, surfaces de ram Riemann-Hilbert, problèmes de ram problème Riemann inriac problème aux limites inriac Boundary value problems Index theory (Mathematics) Riemann surfaces Riemann-Hilbert problems Analytische Funktion (DE-588)4142348-3 gnd Asymptotische Entwicklung (DE-588)4112609-9 gnd Riemannsches Randwertproblem (DE-588)4317184-9 gnd |
| subject_GND | (DE-588)4142348-3 (DE-588)4112609-9 (DE-588)4317184-9 |
| title | Riemann's boundary problem with infinite index |
| title_alt | Kraevaja zadača Rimana s bezkonečnym indeksom |
| title_auth | Riemann's boundary problem with infinite index |
| title_exact_search | Riemann's boundary problem with infinite index |
| title_full | Riemann's boundary problem with infinite index N. V. Govorov |
| title_fullStr | Riemann's boundary problem with infinite index N. V. Govorov |
| title_full_unstemmed | Riemann's boundary problem with infinite index N. V. Govorov |
| title_short | Riemann's boundary problem with infinite index |
| title_sort | riemann s boundary problem with infinite index |
| topic | Functionaalanalyse gtt Index, théorie de l' (Mathématiques) ram Problèmes aux limites ram Riemann, surfaces de ram Riemann-Hilbert, problèmes de ram problème Riemann inriac problème aux limites inriac Boundary value problems Index theory (Mathematics) Riemann surfaces Riemann-Hilbert problems Analytische Funktion (DE-588)4142348-3 gnd Asymptotische Entwicklung (DE-588)4112609-9 gnd Riemannsches Randwertproblem (DE-588)4317184-9 gnd |
| topic_facet | Functionaalanalyse Index, théorie de l' (Mathématiques) Problèmes aux limites Riemann, surfaces de Riemann-Hilbert, problèmes de problème Riemann problème aux limites Boundary value problems Index theory (Mathematics) Riemann surfaces Riemann-Hilbert problems Analytische Funktion Asymptotische Entwicklung Riemannsches Randwertproblem |
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