Solvability theory of boundary value problems and singular integral equations with shift:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
2000
|
| Series: | Mathematics and its applications
523 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 378 S. |
| ISBN: | 0792365496 |
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| 100 | 1 | |a Litvinčuk, Georgij S. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Solvability theory of boundary value problems and singular integral equations with shift |c by Georgii S. Litvinchuk |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 2000 | |
| 300 | |a XVI, 378 S. | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 523 | |
| 650 | 7 | |a Équations intégrales |2 ram | |
| 650 | 4 | |a Boundary value problems |x Numerical solutions | |
| 650 | 4 | |a Integral equations | |
| 650 | 0 | 7 | |a Randwertproblem |0 (DE-588)4048395-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Singuläre Integralgleichung |0 (DE-588)4181523-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Singuläre Integralgleichung |0 (DE-588)4181523-3 |D s |
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| adam_text | IMAGE 1
SOLVABILITY THEORY OF
BOUNDARY VALUE PROBLEMS AND SINGULAR INTEGRAL EQUATIONS WITH SHIFT
BY GEORGII S. LITVINCHUK UNIVERSIDADE DE MADEIRA, DEPARTAMENTO DE
MATEMATICA,
FUNCHAL, PORTUGAL
IIA
FRTOMUEJJJ
ES GIIILJUI JRII
KLUWER ACADEMIC PUBLISHERS
DORDRECHT / BOSTON / LONDON -M ARIJ NI BOINRRT
IMAGE 2
CONTENTS
I N T R O D U C T I ON XI
1 PRELIMINARIES 1
1 ON NOETHER OPERATORS 1
2 SHIFT FUNCTION 4
3 OPERATOR OF SINGULAR INTEGRATION, SHIFT OPERATOR, OPERATOR OF COMPLEX
CONJUGATION AND CERTAIN COMBINATIONS OF THEM 7
4 SINGULAR INTEGRAL OPERATORS WITH CAUCHY KERNEL 13
5 RIEMANN BOUNDARY VALUE PROBLEMS 16
5.1 THE RIEMANN BOUNDARY VALUE PROBLEM ON A SIMPLE CLOSED SMOOTH CONTOUR
FOR ONE UNKNOWN PIECEWISE ANALYTIC FUNCTION 16
5.2 THE RIEMANN BOUNDARY VALUE PROBLEM ON AN OPEN CONTOUR FOR ONE
PIECEWISE ANALYTIC FUNCTION 20
5.3 FACTORIZATION OF MATRIX FUNCTIONS AND THE RIEMANN BOUNDARY VALUE
PROBLEM ON A SIMPLE CLOSED SMOOTH CONTOUR FOR A PIECEWISE ANALYTIC
VECTOR 21
6 THE NOETHER THEORY FOR SINGULAR INTEGRAL OPERATORS WITH A CARLEMAN
SHIFT AND COM PLEX CONJUGATION 25
6.1 SINGULAR INTEGRAL OPERATORS WITH A CARLEMAN SHIFT 25
6.2 SINGULAR INTEGRAL OPERATORS WITH A CARLEMAN SHIFT AND COMPLEX
CONJUGATION 28
2 B I N O M I AL B O U N D A RY VALUE P R O B L E MS W I TH SHIFT FOR A
P I E C E W I SE A N A L Y T IC FUNCTION AND FOR A PAIR OF FUNCTIONS
ANALYTIC IN T HE S A ME D O M A IN 33
7 THE HASEMANN BOUNDARY VALUE PROBLEM 35
7.1 INTEGRAL REPRESENTATION AND SOLUTION OF HASEMANN BOUNDARY VALUE
JUMPPROBLEM 35
7.2 THE CONFORMAL GLUING THEOREM AND REDUCTION OF THE HASEMANN BOUNDARY
VALUE PROBLEM TO THE RIEMANN BOUNDARY VALUE PROBLEM 39
8 BOUNDARY VALUE PROBLEMS WHICH CAN BE REDUCED TO A HASEMANN BOUNDARY
VALUE PROBLEM 44
9 REFERENCES AND A SURVEY OF CLOSELY RELATED RESULTS 45
9.1 REFERENCES 45
9.2 GENERALIZATIONS TO THE CASE OF N PAIRS OF UNKNOWN FUNCTIONS 46
9.3 BOUNDARY VALUE PROBLEMS WITH DISCOUNTINUOUS COEFFICIENTS AND ON OPEN
CONTOURS AND RELATED PROBLEMS 47
9.4 BOUNDARY VALUE PROBLEMS (7.3), (8.1) - (8.3) FOR THE SOLUTIONS OF
LINEAR AND QUASILINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS OF ELLIPTIC
TYPE 53
9.5 LOCAL METHOD OF CONFORMAL GLUING AND ITS APPLICATION TO PROBLEMS
(7.3),
(8.1) - (8.3) CONSIDERED ON CLOSED RIEMANN SURFACES 55
V
IMAGE 3
VI
CONTENTS
3 CARLEMAN B O U N D A RY VALUE P R O B L E MS A ND B O U N D A RY VALUE
P R O B L E MS OF C A R L E M AN T Y PE 59
10 CARLEMAN BOUNDARY VALUE PROBLEMS 60
10.1 STATEMENT OF THE PROBLEM. SOLVABILITY CONDITIONS 60
10.2 INTEGRAL REPRESENTATIONS. SOLUTION OF THE INNER CARLEMAN BOUNDARY
VALUE JUMP-PROBLEM 61
10.3 CONFORMAL GLUING THEOREM 66
10.4 SOLUTION OF THE INNER CARLEMAN BOUNDARY VALUE PROBLEM 70
10.5 EXAMPLE 74
10.6 SOLUTION OF THE OUTER CARLEMAN BOUNDARY VALUE PROBLEM 76
10.7 ULTRADEFINITION OF THE CARLEMAN BOUNDARY VALUE PROBLEM 82
11 BOUNDARY VALUE PROBLEMS OF CARLEMAN TYPE 84
11.1 STATEMENT OF THE PROBLEM. SOLVABILITY CONDITION. HUBERT BOUNDARY
VALUE PROBLEM AS A PARTICULAR CASE OF A BOUNDARY VALUE PROBLEM OF
CARLEMAN TYPE 84 11.2 INTEGRAL REPRESENTATIONS. THE SOLUTION OF THE
INNER BOUNDARY VALUE JUMPPROBLEM OF CARLEMAN TYPE IN THE CASE I) 86
11.3 SOLUTION OF THE INNER HOMOGENEOUS BOUNDARY VALUE PROBLEM OF
CARLEMAN TYPE 91 11.4 THE SOLUTION OF THE INNER NON-HOMOGENEOUS BOUNDARY
VALUE PROBLEM OF CAR LEMAN TYPE 95
11.5 THE SOLUTION OF THE INNER BOUNDARY VALUE PROBLEM OF CARLEMAN TYPE
WITH A(T) = T AND A COEFFICIENT WITH AN ODD CAUCHY INDEX 97
11.6 SOLUTION OF THE OUTER BOUNDARY VALUE PROBLEM OF CARLEMAN TYPE 101
11.7 A BOUNDARY VALUE PROBLEM OF CARLEMAN TYPE WITH THE LINEAR
FRACTIONAL MAPPING OF THE UNIT CIRCLE ONTO ITSELF 109
12 GEOMETRIE INTERPRETATION OF THE CONFORMAL GLUING METHOD 110
13 REFERENCES AND A SURVEY OF CLOSELY RELATED RESULTS 111
13.1 REFERENCES 111
13.2 THE CARLEMAN PROBLEM AND THE PROBLEM OF CARLEMAN TYPE FOR A VECTOR
ANALYTIC IN A DOMAIN AND SOME RELATED PROBLEMS 113
13.3 BOUNDARY VALUE PROBLEMS WITH DISCONTINUOUS COEFFLEIENTS AND A
DISCONTINUOUS DERIVATIVE OF THE SHIFT AND RELATED PROBLEMS 114
13.4 BOUNDARY VALUE PROBLEMS IN THE CLASS OF GENERALIZED ANALYTIC
FUNETIONS . . . 114 13.5 THE CARLEMAN AND CARLEMAN TYPE BOUNDARY VALUE
PROBLEMS FOR DOMAINS OF SPECIAL FORM AND SOME OF ITS APPLICATIONS 115
13.6 IRREGULAER BOUNDARY VALUE PROBLEMS IN THE THEORY OF ANALYTIC
FUNETIONS . . . 117
4 SOLVABILITY T H E O RY OF T HE GENERALIZED R I E M A NN B O U N D A RY
VALUE P R O B L EM 135
14 SOLVABILITY THEORY OF THE GENERALIZED RIEMANN BOUNDARY VALUE PROBLEM
IN THE STABLE AND DEGENERATED CASES 136
14.1 REDUCTION OF THE GENERALIZED RIEMANN BOUNDARY VALUE PROBLEM TO A
RIE MANN BOUNDARY VALUE PROBLEM FOR A TWO-DIMENSIONAL PIEEEWISE
ANALYTIC VECTORL36 14.2 THE SOLVABILITY THEORY OF THE GENERALIZED
RIEMANN BOUNDARY VALUE PROBLEM IN THE STABLE CASE 139
14.3 THE SOLVABILITY THEORY OF THE GENERALIZED RIEMANN BOUNDARY VALUE
PROBLEM IN THE DEGENERATED CASE 141
14.4 THE SOLVABILITY THEORY OF THE 4-NOMIAL GENERALIZED RIEMANN
BOUNDARY VALUE PROBLEMS IN THE STABLE AND DEGENERATED CASES 143
14.5 ON THE STABILITY OF BOUNDARY VALUE PROBLEMS 144
15 REFERENCES AND A SURVEY OF SIMILAR OR RELATED RESULTS 145
15.1 REFERENCES 145
IMAGE 4
CONTENTS
VII
15.2 SURVEY OF SOME RESULTS CONCERNING THE SOLVABILITY THEORY OF
GENERALIZED RIEMANN BOUNDARY VALUE PROBLEMS WITH HOLDER COEFFICIENTS 147
15.3 GENERALIZED RIEMANN BOUNDARY VALUE PROBLEM WITH MEASURABLE
COEFFICIENTS IN THE SPACE L P, 1 P OO 150
15.4 GENERALIZED RIEMANN BOUNDARY VALUE PROBLEM WITH CONTINUOUS AND
PIECEWISE CONTINUOUS COEFFICIENTS ON A SIMPLE AND ON A COMPOSITE CONTOUR
153
15.5 SOME OTHER GENERALIZATIONS AND VARIANTS OF THE PROBLEM 154
15.6 AUXILIARY INFORMATION FROM THE THEORY OF BEST APPROXIMATIONS IN THE
CLASSES HO6 AND S-NUMBERS OF HANKEL OPERATORS 155
15.7 FACTORIZATION OF HERMITIAN MATRIX FUNCTIONS 157
15.8 EXACT ESTIMATES OF THE DEFECT NUMBERS AND A CLASSIFICATION OF THE
GENERALIZED RIEMANN BOUNDARY VALUE PROBLEM 162
15.9 PROBLEMS OF UNIFORM APPROXIMATIONS WITH PARTIALLY FIXED POLES 165
15.10 GENERALIZED RIEMANN BOUNDARY VALUE PROBLEM WITH A SHIFT 170
15.11 BOUNDARY VALUE PROBLEM (14.1) AND ITS GENERALIZATIONS FOR
SOLUTIONS OF LINEAR AND QUASI-LINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS
173
15.12 APPLICATIONS OF BOUNDARY VALUE PROBLEM (14.1) AND ITS
GENERALIZATIONS TO THE PROBLEM OF INFINITESIMAL DEFORMATIONS OF SURFACES
WITH POSITIVE CURVATURE 173 15.13 APPLICATIONS TO THE DISTRIBUTION OF
PHYSICAL FIELDS 175
SOLVABILITY T H E O RY OF SINGULAR INTEGRAL E Q U A T I O NS W I TH A C
A R L E M AN SHIFT AND
C O M P L EX C O N J U G A T ED B O U N D A RY VALUES IN T HE D E G E N
E R A T ED A ND S T A B LE CASES 177
16 CHARACTERISTIC SINGULAR INTEGRAL EQUATION WITH A CARLEMAN SHIFT IN
THE DEGENERATED CASES 178
16.1 NOETHERITY CONDITIONS AND INDEX FORMULA OF A 4-NOMIAL BOUNDARY
VALUE PRO BLEM WITH A CARLEMAN SHIFT 178
16.2 THE DEGENERATED CASE OF A 4-NOMIAL PROBLEM WITH AN INVERSE CARLEMAN
SHIFT AS A SYSTEM OF TWO INDEPENDENT CARLEMAN BOUNDARY VALUE PROBLEMS .
. .. 179
16.3 T HE DEGENERATED CASE OF A 4-NOMIAL PROBLEM WITH AN INVERSE
CARLEMAN SHIFT AS A SYSTEM OF TWO DEPENDENT CARLEMAN BOUNDARY VALUE
PROBLEMS 183
16.4 THE DEGENERATED CASE OF A 4-NOMIAL PROBLEM WITH A DIRECT CARLEMAN
SHIFT AS A HASEMANN BOUNDARY VALUE PROBLEM 184
16.5 THE DEGENERATED CASE OF A 4-NOMIAL PROBLEM WITH A CARLEMAN SHIFT AS
A
RIEMANN BOUNDARY VALUE PROBLEM 184
16.6 SPECIAL CASES OF A CHARACTERISTIC SINGULAR INTEGRAL EQUATION WITH A
CARLEMAN SHIFT 185
17 CHARACTERISTIC SINGULAR INTEGRAL EQUATION WITH A CARLEMAN SHIFT AND
COMPLEX CONJUGATION IN THE DEGENERATED CASES 188
17.1 NOETHERITY CONDITIONS AND INDEX FORMULA OF A 4-NOMIAL BOUNDARY
VALUE PRO BLEM WITH A CARLEMAN SHIFT AND COMPLEX CONJUGATED BOUNDARY
VALUES . . . 188 17.2 THE DEGENERATED CASE OF A 4-NOMIAL PROBLEM WITH A
DIRECT CARLEMAN SHIFT AND COMPLEX CONJUGATED BOUNDARY VALUES AS A SYSTEM
OF TWO INDEPENDENT
PROBLEMS OF CARLEMAN TYPE 189
17.3 T HE DEGENERATED CASE OF A 4-NOMIAL PROBLEM WITH A DIRECT CARLEMAN
SHIFT AND COMPLEX CONJUGATED BOUNDARY VALUES AS A SYSTEM OF TWO
DEPENDENT PROBLEMS OF CARLEMAN TYPE 192
17.4 THE DEGENERATED CASES OF A 4-NOMIAL PROBLEM WITH A CARLEMAN SHIFT
AND COMPLEX CONJUGATED BOUNDARY VALUES AS A PROBLEM OF HASEMANN TYPE AND
AS A RIEMANN BOUNDARY VALUE PROBLEM 193
18 SOLVABILITY THEORY OF A SINGULAR INTEGRAL EQUATION WITH A CARLEMAN
SHIFT AND COMPLEX CONJUGATION IN THE STABLE CASES 194
IMAGE 5
VIII CONTENTS
18.1 BOUNDARY VALUE PROBLEM WITH CARLEMAN SHIFT AND COMPLEX CONJUGATED
BOUN DARY VALUES IN THE STABLE CASES 194
18.2 BOUNDARY VALUE PROBLEM WITH A CARLEMAN SHIFT IN THE STABLE CASES
200
19 REFERENCES AND A SURVEY OF SIMILAR OR RELATED RESULTS 202
19.1 REFERENCES - 202
19.2 SURVEY OF SIMILAR OR RELATED RESULTS 202
SOLVABILITY THEORY OF GENERAL CHARACTERISTIC SINGULAR INTEGRAL E Q U A T
I O NS W I TH A CARLEMAN FRACTIONAL LINEAR SHIFT ON T HE UNIT CIRCLE 207
20 CHARACTERISTIC SINGULAR INTEGRAL EQUATION WITH A DIRECT CARLEMAN
FRACTIONAL LINEAR SHIFT 208
20.1 LEADING REASONING AND STATEMENT OF THE FACTORIZATION PROBLEM 208
20.2 FACTORIZATION OF MATRIX FUNCTIONS IN THE SUBALGEBRA H 2 X2 211
20.3 FACTORIZATION OF SINGULAR INTEGRAL OPERATOR T(A) 218
21 CHARACTERISTIC SINGULAR INTEGRAL EQUATION WITH AN INVERSE CARLEMAN
FRACTIONAL LINEAR SHIFT 226
21.1 STATEMENT OF THE FACTORIZATION PROBLEM. THE RELATION B = EA(A)E AND
ITS
CONSEQUENCES 226
21.2 FACTORIZATION OF THE SINGULAR INTEGRAL OPERATOR WITH SHIFT T 230
21.3 ONE SPECIAL CASE OF A SINGULAR INTEGRAL OPERATOR WITH CARLEMAN
FRACTIONAL LINEAR SHIFT A = O?_(T) 239
22 REFERENCES AND SURVEY OF CLOSED AND RELATED RESULTS 242
22.1 REFERENCES 242
22.2 SOLVABILITY THEORY OF SINGULAR INTEGRAL EQUATIONS WITH THE
OPERATORS OF WEIGHTED FRACTIONAL LINEAR CARLEMAN SHIFT AND COMPLEX
CONJUGATION. GENERALIZATION TO THE CASE OF MATRIX COEFFICIENTS 242
22.3 SPECTRUM PROBLEMS FOR SINGULAR INTEGRAL OPERATORS WITH CARLEMAN
SHIFT . . . 246
GENERALIZED H U B E RT A ND C A R L E M AN B O U N D A RY VALUE P R O B
L E MS FOR FUNCTIONS ANALYTIC IN A SIMPLY C O N N E C T ED D O M A IN
251
23 NOETHER THEORY OF A GENERALIZED HUBERT BOUNDARY VALUE PROBLEM 252
23.1 STATEMENT OF THE PROBLEM 252
23.2 REDUCTION OF A GENERALIZED HUBERT BOUNDARY VALUE PROBLEM TO A
SINGULAR INTEGRAL EQUATION WITH CARLEMAN SHIFT 253
23.3 CONSTRUCTING THE ALLIED BOUNDARY VALUE PROBLEM. THE SOLVABILITY
CONDITIONS OF A GENERALIZED HUBERT BOUNDARY VALUE PROBLEM 254
23.4 NOETHERITY CONDITIONS AND THE INDEX FORMULA OF A GENERALIZED HUBERT
BOUN DARY VALUE PROBLEM 258
23.5 EXAMPLES 258
24 SOLVABILITY THEORY OF GENERALIZED HUBERT BOUNDARY VALUE PROBLEMS 263
24.1 STATEMENT OF THE PROBLEMS. THE MAIN IDENTITIES 263
24.2 THE DEGENERATING CASE OF A GENERALIZED HUBERT BOUNDARY VALUE
PROBLEM AS A PROBLEM OF CARLEMAN TYPE 264
24.3 THE DEGENERATING CASE OF A GENERALIZED HUBERT BOUNDARY VALUE
PROBLEM AS A USUAL HUBERT PROBLEM 265
24.4 THE DEGENERATING CASE OF A GENERALIZED HUBERT BOUNDARY VALUE
PROBLEM AS A CARLEMAN PROBLEM 266
25 NOETHERITY THEORY OF A GENERALIZED CARLEMAN BOUNDARY VALUE PROBLEM
267
25.1 STATEMENT OF THE PROBLEM. CONDITIONS ELIMINATING THE
ULTRADEFLNITION OF THE PROBLEM 267
IMAGE 6
CONTENTS
IX
25.2 AUXILIARY BOUNDARY VALUE PROBLEM FOR TWO FUNCTIONS ANALYTIC IN THE
DOMAIN D +. CONNECTION BETWEEN THE SOLVABILITY OF A GENERALIZED CARLEMAN
BOUNDARY VALUE PROBLEM AND OF THE AUXILIARY ONE 270
25.3 THE NOETHER THEORY OF THE AUXILIARY PROBLEM IN THE CASE A = A +(T)
271
25.4 THE NOETHER THEORY OF THE AUXILIARY PROBLEM IN THE CASE A = A _ (
I) 274
25.5 THE NOETHERITY CONDITIONS AND THE INDEX FORMULA OF A GENERALIZED
CARLEMAN BOUNDARY VALUE PROBLEM 278
25.6 EXAMPLE 283
26 SOLVABILITY THEORY OF A GENERALIZED CARLEMAN BOUNDARY VALUE PROBLEM
285
26.1 A THEOREM ON SOLVABILITY IN THE CASE OF A DIRECT CARLEMAN SHIFT 286
26.2 A THEOREM ON SOLVABILITY IN THE CASE OF AN INVERSE CARLEMAN SHIFT
288
27 REFERENCES AND A SURVEY OF SIMILAR OR RELATED RESULTS 290
27.1 REFERENCES 290
27.2 GENERALIZED CARLEMAN BOUNDARY VALUE PROBLEM IN THE WEIGHTED SPACES
L P, 1 P OO 290
27.3 GENERAL BOUNDARY VALUE PROBLEM WITH A CARLEMAN SHIFT AND
CONJUGATION FOR ONE FUNCTION ANALYTIC IN A SIMPLY-CONNECTED DOMAIN 296
27.4 INNER POLYNOMIAL BOUNDARY VALUE PROBLEMS FOR TWO FUNCTIONS OR
VECTORS. . . 296 27.5 BOUNDARY VALUE PROBLEMS FOR FUNCTIONS PIECEWISE
ANALYTIC IN A DOMAIN. . . . 297 27.6 THE OPERATOR APPROACH FOR THE
INVESTIGATION OF BOUNDARY VALUE PROBLEMS FOR FUNCTIONS ANALYTIC IN THE
SAME DOMAIN 299
8 B O U N D A RY VALUE P R O B L E MS W I TH A C A R L E M AN SHIFT AND
C O M P L EX C O N J U G A T I ON FOR
FUNCTIONS A N A L Y T IC IN A M U L T I P LY C O N N E C T ED D O M A IN
303
28 INTEGRAL REPRESENTATIONS OF FUNCTIONS ANALYTIC IN A MULTIPLY
CONNECTED DOMAIN . . . 304 28.1 SOME NOTATIONS AND DEFINITIONS 304
28.2 INTEGRAL REPRESENTATION WITH A DENSITY DEPENDING ON A CARLEMAN
SHIFT A = A+(T) 304
28.3 INTEGRAL REPRESENTATION WITH A DENSITY DEPENDING ON A CARLEMAN
SHIFT A = A _ ( I) 307
29 THE NOETHER THEORY OF A GENERALIZED CARLEMAN BOUNDARY VALUE PROBLEM
WITH A DIRECT SHIFT A = A +(T) IN A MULTIPLY CONNECTED DOMAIN 309
30 THE SOLVABILITY THEORY OF A BINOMIAL BOUNDARY VALUE PROBLEM OF
CARLEMAN TYPE IN A MULTIPLY CONNECTED DOMAIN 314
30.1 THE MAIN LEMMAS 314
30.2 CALCULATION OF THE NUMBER OF LINEARLY INDEPENDENT SOLUTIONS IN THE
CASES K 0 AND K 2M - 2 318
30.3 SHARP ESTIMATES FOR THE NUMBER / OF LINEARLY INDEPENDENT SOLUTIONS
OF A
BOUNDARY VALUE PROBLEM OF CARLEMAN TYPE IN THE CASE 0 K IM - 2 . . .
319
31 THE SOLVABILITY THEORY OF A CARLEMAN BOUNDARY VALUE PROBLEM IN A
MULTIPLY CON NECTED DOMAIN 321
31.1 THE SOLUTION OF A CARLEMAN BOUNDARY VALUE PROBLEM WITH A JUMP IN A
MUL TIPLY CONNECTED DOMAIN OF TYPE M 321
31.2 CONFORMAL GLUING THEOREM 324
31.3 CALCULATION OF DEFECT NUMBERS 324
32 THE NOETHER THEORY OF A GENERALIZED CARLEMAN BOUNDARY VALUE PROBLEM
WITH AN INVERSE SHIFT A = A_ FOR A MULTIPLY CONNECTED DOMAIN 326
33 REFERENCES AND A SURVEY OF SIMILAR OR RELATED RESULTS 329
33.1 REFERENCES 329
33.2 SOME OTHER RESULTS ON THE THEORY OF BOUNDARY VALUE PROBLEMS FOR
FUNCTIONS ANALYTIC IN A MULTIPLY-CONNECTED DOMAIN OF TYPE M 329
IMAGE 7
X
CONTENTS
33.3 BOUNDARY VALUE PROBLEMS WITH MIXED BOUNDARY CONDITIONS 330
33.4 GENERAL BOUNDARY VALUE PROBLEMS WITH SHIFT, COMPLEX CONJUGATION AND
DE RIVATIVES FOR FUNCTIONS ANALYTIC IN A MULTIPLY-CONNECTED DOMAIN 331
33.5 A CARLEMAN BOUNDARY VALUE PROBLEM, A BOUNDARY VALUE PROBLEM OF
CARLEMAN TYPE AND SOME OF THEIR GENERALIZATIONS AND MODIFICATIONS ON A
RIEMANN SURFACE WITH BOUNDARY. 333
33.6 ON BOUNDARY VALUE PROBLEMS IN THE CLASS OF GENERALIZED ANALYTIC
FUNCTIONS . 338 33.7 BOUNDARY VALUE PROBLEMS WITH A SHIFT AND A COMPLEX
CONJUGATION ON A NON COMPACT (OPEN) RIEMANN SURFACES IN THE CLASS OF
ANALYTIC FUNCTIONS AND FOR SOLUTIONS OF A LINEAR SYSTEM OF ELLIPTIC TYPE
EQUATIONS 339
33.8 APPLICATION OF A 3-NOMIAL BOUNDARY VALUE PROBLEM WITH SHIFT TO THE
ELASTICITY THEORY OF ANISOTROPIC SOLIDS 340
9 ON SOLVABILITY T H E O RY FOR SINGULAR INTEGRAL E Q U A T I O NS W I
TH A N O N - C A R L E M AN SHIFT343 34 AUXILIARY LEMMAS 344
35 ESTIMATE FOR THE DIMENSION OF THE KERNEL OF A SINGULAR INTEGRAL
OPERATOR WITH A
NON-CARLEMAN SHIFT HAVING A FMITE NUMBER OF FLXED POINTS 349
36 APPROXIMATE SOLUTION OF A NON-HOMOGENEOUS SINGULAR INTEGRAL EQUATION
WITH A NONCARLEMAN SHIFT 351
37 SINGULAR INTEGRAL EQUATIONS WITH NON-CARLEMAN SHIFT AS A NATURAL
MODEL FOR PROBLEMS OF SYNTHESIS OF SIGNALS FOR LINEAR SYSTEMS WITH
NON-STATIONARY PARAMETERS 353
REFERENCES 355
S U B J E CT I N D EX 377
|
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| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV013869259 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:53:28Z |
| institution | BVB |
| isbn | 0792365496 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009486633 |
| oclc_num | 491522952 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | XVI, 378 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Kluwer |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Litvinčuk, Georgij S. Verfasser aut Solvability theory of boundary value problems and singular integral equations with shift by Georgii S. Litvinchuk Dordrecht [u.a.] Kluwer 2000 XVI, 378 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 523 Équations intégrales ram Boundary value problems Numerical solutions Integral equations Randwertproblem (DE-588)4048395-2 gnd rswk-swf Singuläre Integralgleichung (DE-588)4181523-3 gnd rswk-swf Singuläre Integralgleichung (DE-588)4181523-3 s Randwertproblem (DE-588)4048395-2 s DE-604 Mathematics and its applications 523 (DE-604)BV008163334 523 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009486633&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Litvinčuk, Georgij S. Solvability theory of boundary value problems and singular integral equations with shift Mathematics and its applications Équations intégrales ram Boundary value problems Numerical solutions Integral equations Randwertproblem (DE-588)4048395-2 gnd Singuläre Integralgleichung (DE-588)4181523-3 gnd |
| subject_GND | (DE-588)4048395-2 (DE-588)4181523-3 |
| title | Solvability theory of boundary value problems and singular integral equations with shift |
| title_auth | Solvability theory of boundary value problems and singular integral equations with shift |
| title_exact_search | Solvability theory of boundary value problems and singular integral equations with shift |
| title_full | Solvability theory of boundary value problems and singular integral equations with shift by Georgii S. Litvinchuk |
| title_fullStr | Solvability theory of boundary value problems and singular integral equations with shift by Georgii S. Litvinchuk |
| title_full_unstemmed | Solvability theory of boundary value problems and singular integral equations with shift by Georgii S. Litvinchuk |
| title_short | Solvability theory of boundary value problems and singular integral equations with shift |
| title_sort | solvability theory of boundary value problems and singular integral equations with shift |
| topic | Équations intégrales ram Boundary value problems Numerical solutions Integral equations Randwertproblem (DE-588)4048395-2 gnd Singuläre Integralgleichung (DE-588)4181523-3 gnd |
| topic_facet | Équations intégrales Boundary value problems Numerical solutions Integral equations Randwertproblem Singuläre Integralgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009486633&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT litvincukgeorgijs solvabilitytheoryofboundaryvalueproblemsandsingularintegralequationswithshift |