Equations with involutive operators:
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2001
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 395 - 418 |
| Physical Description: | XXII, 427 S. 24 cm |
| ISBN: | 3764341572 0817641572 |
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| 100 | 1 | |a Karapetjanc, Nikolaj K. |d 1942- |e Verfasser |0 (DE-588)123081963 |4 aut | |
| 245 | 1 | 0 | |a Equations with involutive operators |c Nikolai Karapetiants ; Stefan Samko |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2001 | |
| 300 | |a XXII, 427 S. |b 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz. S. 395 - 418 | ||
| 650 | 4 | |a Fredholm operators | |
| 650 | 4 | |a Integral equations | |
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| 700 | 1 | |a Samko, Stefan G. |e Verfasser |4 aut | |
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Record in the Search Index
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| adam_text | NIKOLAI KARAPETIANTS STEFAN SAMKO EQUATIONS WITH INVOLUTIVE OPERATORS
BIRKHAUSER BOSTON * BASEL * BERLIN CONTENTS INTRODUCTION XV NOTATION XXI
1 ON FREDHOLMNESS OF SINGULAR TYPE OPERATORS 1 1 FREDHOLM OPERATORS 1
1.1 BASICS ON FREDHOLM OPERATORS 1 1.2 FREDHOLMNESS OF OPERATORS WITH
PROJECTORS 5 1.3 FREDHOLMNESS OF MATRIX OPERATORS 9 2 SINGULAR INTEGRAL
OPERATORS WITH PIECEWISE CONTINUOUS COEFFICIENTS IN THE SPACE L P (T) 14
2.1 SINGULAR INTEGRAL OPERATORS IN THE SPACE L P (T) 14 2.2 THE NOTION
OF P-INDEX 16 2.3 FREDHOLMNESS CRITERION AND THE INDEX FORMULA 21 2.4
APPROXIMATION OF NON-FREDHOLM OPERATORS BY FREDHOLM ONES 24 2.5 ON
COMPACTNESS OF SOME COMPOSITE SINGULAR OPERATORS 25 3 ON FREDHOLMNESS
OF CONVOLUTION TYPE OPERATORS 26 3.1 FOURIER TRANSFORMS AND THE WIENER
ALGEBRA 26 3.2 GENERAL PRELIMINARIES ON CONVOLUTION OPERATORS 30 3.3
THEOREMS ON FREDHOLMNESS 34 3.4 ON COMPACTNESS OF SOME CONVOLUTION TYPE
OPERATORS . . 36 VIII CONTENTS 3.5 ON FREDHOLMNESS OF CONVOLUTION TYPE
OPERATORS WITH VARIABLE COEFFICIENTS 41 3.6 DISCRETE CONVOLUTION TYPE
EQUATIONS 43 3.7 ON HANKEL OPERATORS 45 4 BIBLIOGRAPHIC NOTES TO CHAPTER
1 48 2 ON FREDHOLMNESS OF OTHER SINGULAR-TYPE OPERATORS 51 5 ON
OPERATORS WITH HOMOGENEOUS KERNELS; THE ONE-DIMENSIONAL CASE 51 5.1
CONNECTION WITH CONVOLUTION OPERATORS; L P -BOUNDEDNESS 52 5.2 ON
FREDHOLMNESS OF THE OPERATORS XI * K 53 5.3 THE CARLEMAN EQUATION AND
NOTION OF THE STANDARD A-LEMNISCATE 65 6 OPERATORS WITH HOMOGENEOUS
KERNELS; THE MULTI-DIMENSIONAL CASE 68 6.1 LP-BOUNDEDNESS 69 6.2 ON
SPHERICAL HARMONICS 72 6.3 FORMAL REDUCTION TO A SYSTEM OF
ONE-DIMENSIONAL EQUATIONS WITH HOMOGENEOUS KERNELS 75 6.4 JUSTIFICATION
OF THE REDUCTION AND THE MAIN RESULT FOR ROTATION INVARIANT HOMOGENEOUS
KERNELS 77 6.5 SOME CASES OF NON-ROTATION INVARIANT KERNELS AND OTHER
TYPES OF HOMOGENEITY 82 7 CONVOLUTION-TYPE OPERATORS WITH DISCONTINUOUS
SYMBOLS . . . . 84 7.1 SETTING OF THE PROBLEM 85 7.2 LIZORKIN SPACE 86
7.3 FRACTIONAL INTEGRATION OF LIOUVILLE AND BESSEL TYPE ... 87 7.4 THE
CASE OF A CONTINUOUS SYMBOL 90 7.5 THE CASE OF A DISCONTINUOUS
COEFFICIENT G(X) 93 7.6 FOURIER TRANSFORM OF A CERTAIN FUNCTION 94 7.7
ON A SPECIAL GROUP OF OPERATORS 95 7.8 THE MODEL OPERATOR WITH A
DISCONTINUOUS SYMBOL . . . . 98 7.9 THE CASE G(X) = 1 100 7.10 THE
GENERAL CASE OF A DISCONTINUOUS SYMBOL 101 8 BIBLIOGRAPHIC NOTES TO
CHAPTER 2 109 3 FUNCTIONAL AND SINGULAR INTEGRAL EQUATIONS WITH CARLEMAN
SHIFTS IN THE CASE OF CONTINUOUS COEFFICIENTS 111 9 CARLEMAN AND
GENERALIZED CARLEMAN SHIFTS ILL 9.1 ON SOME PROPERTIES OF SHIFTS ILL 9.2
ON A()-FACTORIZATION OF FUNCTIONS 114 9.3 THE WINDING NUMBER OF
FUNCTIONS, INVARIANT AND ANTI-INVARIANT WITH RESPECT TO SHIFT 118 9.4 ON
A(T)-FACTORIZATION IN THE CASE OF THE SHIFT A(T) = TE XU ON THE UNIT
CIRCLE 119 9.5 LOGARITHMIC MEANS AND FACTORIZATION 124 CONTENTS IX 9.6
FACTORIZATION WITH THE SHIFT X + H ON THE REAL LINE . . . . 127 10 A
FUNCTIONAL EQUATION WITH SHIFT 128 10.1 CONNECTION BETWEEN A FUNCTIONAL
EQUATION WITH SHIFT AND AN ALGEBRAIC SYSTEM 129 10.2 FUNCTIONAL
EQUATIONS IN THE DEGENERATE CASE 131 10.3 FUNCTIONAL EQUATIONS WITH THE
SHIFT A(T) * TE IOJ 134 10.4 SOME GENERALIZATIONS 139 11 SINGULAR
INTEGRAL EQUATIONS WITH CARLEMAN SHIFT ON A CLOSED CURVE; THE CASE OF
CONTINUOUS COEFFICIENTS 142 11.1 ACCOMPANYING AND ASSOCIATED OPERATORS
142 11.2 FREDHOLMNESS THEOREM; THE CASE OF PRESERVATION OF THE
ORIENTATION 144 11.3 FREDHOLMNESS THEOREM; THE CASE OF CHANGE OF THE
ORIENTATION 145 11.4 ON REGULARIZERS OF SINGULAR OPERATORS WITH SHIFT
146 12 SINGULAR INTEGRAL EQUATIONS WITH CARLEMAN SHIFT ON AN OPEN CURVE;
THE CASE OF CONTINUOUS COEFFICIENTS 147 12.1 THE PASSAGE TO A
COMPOSITE SINGULAR INTEGRAL OPERATOR 147 12.2 REPRESENTATION OF A
COMPOSITE SINGULAR INTEGRAL OPERATOR AS A COMPOSITION OF USUAL
SINGULAR OPERATORS . . 149 12.3 FREDHOLMNESS THEOREM FOR THE OPERATOR
(12.1) 150 13 BIBLIOGRAPHIC NOTES TO CHAPTER 3 151 4 TWO-TERM EQUATIONS
(A + QB)IP = / WITH AN INVOLUTIVE OPERATOR Q; AN ABSTRACT APPROACH AND
APPLICATIONS 153 14 FREDHOLMNESS OF AN ABSTRACT EQUATION WITH AN
INVOLUTIVE OPERATOR; NON-MATRIX APPROACH 154 14.1 PROMPTING IDEAS 154
14.2 A SYSTEM OF AXIOMS. EXAMPLES 155 14.3 FREDHOLMNESS THEOREM 157 14.4
INVERTIBILITY THEOREM 161 15 APPLICATION TO SINGULAR INTEGRAL EQUATIONS
WITH COMPLEX CONJUGATE UNKNOWNS 162 15.1 ANTI-QUASICOMMUTATION OF THE
OPERATORS Q AND 5 . ... 162 15.2 THE CASE OF A CLOSED CURVE 163 15.3 THE
CASE OF AN OPEN CURVE 164 16 APPLICATIONS TO INTEGRAL EQUATIONS ON THE
REAL LINE WITH REFLECTION OR INVERSION 165 16.1 CONVOLUTION TYPE
EQUATIONS WITH REFLECTION 165 16.2 THE CASE OF WEIGHTED SPACES 167 16.3
SINGULAR CONVOLUTION OPERATORS WITH REFLECTION 172 16.4 CONVOLUTION TYPE
OPERATORS WITH A DISCONTINUOUS SYMBOL AND REFLECTION 173 16.5 EQUATIONS
WITH HOMOGENEOUS KERNELS AND THE SHIFT - . . 176 CONTENTS 16.6 .
DISCRETE ANALOGUE OF CONVOLUTION EQUATIONS WITH REFLECTION 178 17
APPLICATION TO SINGULAR INTEGRAL EQUATIONS WITH CARLEMAN SHIFT ON AN
OPEN CURVE; THE CASE OF DISCONTINUOUS COEFFICIENTS 179 17.1 THE NORMED
OPERATOR 180 17.2 REDUCTION OF THE NORMED OPERATOR TO A COMPOSITE
SINGULAR OPERATOR 180 17.3 REPRESENTATION OF A COMPOSITE SINGULAR
OPERATOR AS A COMPOSITION OF USUAL SINGULAR OPERATORS AND THE THEOREM ON
FREDHOLMNESS OF THE COMPOSITE OPERATOR 182 17.4 THEOREM ON
FREDHOLMNESS OF THE NORMED OPERATOR . . . 186 17.5 THEOREM ON
FREDHOLMNESS IN THE GENERAL CASE 186 18 SINGULAR INTEGRAL EQUATIONS WITH
A FRACTIONAL LINEAR SHIFT IN THE SPACE L P WITH A SPECIAL WEIGHT 188
18.1 THE CHOICE OF THE WEIGHTED SPACE AND CONSTRUCTION OF THE INVOLUTIVE
OPERATOR 189 18.2 THE CASE OF SHIFT PRESERVING THE ORIENTATION (D 0) .
. 1912 18.3 THE CASE OF SHIFT CHANGING THE ORIENTATION (D 0) ... 192
19 FREDHOLMNESS OF ABSTRACT EQUATIONS WITH A GENERALIZED INVOLUTIVE
OPERATOR (NON-MATRIX APPROACH) 193 19.1 SYSTEM OF AXIOMS AND THE THEOREM
ON FREDHOLMNESS . . 193 19.2 ON DEFICIENCY NUMBERS OF THE OPERATOR K = A
+ QB . . 197 19.3 APPLICATION TO DISCRETE WIENER-HOPF EQUATIONS WITH
OSCILLATING COEFFICIENTS 199 19.4 APPLICATION TO PAIRED DISCRETE
CONVOLUTION TYPE EQUATIONS WITH OSCILLATING COEFFICIENTS 202 19.5 THE
CASE OF IRRATIONAL OSCILLATION 203 20 ABSTRACT EQUATIONS WITH ALGEBRAIC
OPERATORS 206 20.1 ON A PARTITION OF UNITY 207 20.2 ALGEBRAIC OPERATORS.
EQUATIONS WITH SUCH OPERATORS IN THE CASE OF CONSTANT COEFFICIENTS 208
20.3 THE NILPOTENT CASE 212 20.4 REGULARIZATION OF EQUATIONS WITH
QUASI-ALGEBRAIC OPERA- TORS IN THE CASE OF OPERATOR COEFFICIENTS 213
20.5 THE CHARACTERISTIC PART OF EQUATIONS WITH ALGEBRAIC OPERATORS 215
20.6 APPLICATION TO A FUNCTIONAL EQUATION WITH THE FOURIER TRANSFORM 218
21 BIBLIOGRAPHIC NOTES TO CHAPTER 4 219 EQUATIONS WITH SEVERAL
GENERALIZED INVOLUTIVE OPERATORS. MATRIX ABSTRACT APPROACH AND
APPLICATIONS 223 22 FREDHOLMNESS OF ABSTRACT EQUATIONS WITH GENERALIZED
INVOLUTIVE OPERATORS (MATRIX APPROACH) 223 CONTENTS XI 22.1 THE CASE OF
ONE GENERALIZED INVOLUTIVE OPERATOR 224 22.2 A SCHEME OF INVESTIGATION
OF EQUATIONS WITH TWO GENERALIZED INVOLUTIVE OPERATORS (REDUCTION) . .
231 22.3 CONNECTIONS BETWEEN MATRIX AND NON-MATRIX APPROACHES 239 23
SINGULAR INTEGRAL EQUATIONS WITH A FINITE GROUP OF SHIFTS IN THE CASE OF
CONTINUOUS COEFFICIENTS 244 23.1 THE EQUATION WITH ONE GENERALIZED
CARLEMAN SHIFT . . . 245 23.2 CLASSIFICATION OF A FINITE GROUP OF SHIFTS
ON CLOSED OR OPEN CURVES 246 23.3 SINGULAR INTEGRAL EQUATIONS ON A
CLOSED CURVE WITH TWO SHIFTS 248 24 SINGULAR INTEGRAL EQUATIONS WITH A
FINITE GROUP OF SHIFTS (THE CASE OF PIECEWISE CONTINUOUS COEFFICIENTS)
253 24.1 THE CASE OF A CLOSED CURVE 252 24.2 THE CASE OF ONE SHIFT,
CHANGING THE ORIENTATION ON A CLOSED CURVE 256 24.3 THE CASE OF AN OPEN
CURVE 258 24.4 SINGULAR INTEGRAL EQUATIONS WITH SHIFT AND COMPLEX
CONJUGATION 259 25 CONVOLUTION TYPE EQUATIONS WITH SHIFTS AND COMPLEX
CONJUGATION 261 25.1 DISCRETE CONVOLUTION OPERATORS WITH ALMOST
STABILIZING COEFFICIENTS 261 25.2 FREDHOLMNESS OF DISCRETE CONVOLUTION
OPERATORS WITH OSCILLATION AND REFLECTION 265 25.3 CONVOLUTION TYPE
EQUATIONS WITH REFLECTION AND COMPLEX CONJUGATION 267 25.4 INTEGRAL
EQUATIONS WITH HOMOGENEOUS KERNELS INVOLVING TERMS WITH INVERSION AND
COMPLEX CONJUGATION 270 26 BIBLIOGRAPHIC NOTES TO CHAPTER 5 273 6
APPLICATION OF THE ABSTRACT APPROACH TO SINGULAR EQUATION ON THE REAL
LINE WITH FRACTIONAL LINEAR SHIFT 275 27 SINGULAR INTEGRAL OPERATORS
PERTURBED BY INTEGRAL OPERATORS WITH HOMOGENEOUS KERNELS 277 27.1 SOME
NECESSARY CONDITIONS 278 27.2 REDUCTION TO A SYSTEM OF PAIRED
CONVOLUTION EQUATIONS . 279 27.3 SYSTEMS OF SINGULAR INTEGRAL EQUATIONS
PERTURBED BY INTEGRALS WITH HOMOGENEOUS KERNELS 284 28 SINGULAR INTEGRAL
OPERATORS WITH A FRACTIONAL LINEAR CARLEMAN SHIFT IN THE WEIGHTED SPACE
L^(R X ) 287 28.1 SETTING OF THE PROBLEM AND INTRODUCTION OF THE
INVOLUTIVE OPERATOR Q^ 288 28.2 SOME CONNECTIONS BETWEEN THE INVOLUTIVE
OPERATOR Q U AND THE SINGULAR INTEGRAL OPERATORS S, S A AND S A . . .
. 289 XII CONTENTS 28.3 REDUCTION OF SINGULAR INTEGRAL EQUATIONS WITH A
FRACTIONAL LINEAR SHIFT TO A SYSTEM OF PERTURBED SINGULAR EQUATIONS
WITHOUT SHIFT 294 28.4 THE CASE OF PRESERVATION OF THE ORIENTATION (D
0) . . . 297 28.5 THE CASE OF CHANGE OF THE ORIENTATION (D 0) 304 28.6
THE INVESTIGATION OF EQUATION (B) 305 28.7 THE CASE OF A NONFRACTIONAL
LINEAR SHIFT ON R 1 309 29 EQUATIONS INCLUDING OPERATORS WITH
HOMOGENEOUS KERNELS, THE SINGULAR INTEGRAL OPERATORS AND THE INVERSION
SHIFT 311 30 POTENTIAL TYPE OPERATORS ON THE REAL 1 INE WITH A
FRACTIONAL LINEAR CARLEMAN SHIFT 316 30.1 ON NORMAL SOLVABILITY OF
POTENTIAL TYPE OPERATORS WITH DISCONTINUOUS CHARACTERISTICS 317 30.2 THE
CASE OF LINEAR SHIFT (THE CASE OF REFLECTION) 319 30.3 THE CASE OF
FRACTIONAL LINEAR SHIFT 321 31 GENERALIZED CARLEMAN FRACTIONAL LINEAR
SHIFTS ON THE REAL LINE . . 326 31.1 ITERATIONS OF FRACTIONAL LINEAR
SHIFTS AND ITS PROPERTIES . . 326 31.2 SOME ADDITIONAL PROPERTIES OF
FRACTIONAL LINEAR SHIFTS *. . 330 31.3 ON A FINITE GROUP OF FRACTIONAL
LINEAR TRANSFORMATIONS . . 331 32 SINGULAR INTEGRAL EQUATIONS WITH A
GENERALIZED CARLEMAN FRACTIONAL LINEAR SHIFT 333 33 BIBLIOGRAPHIC NOTES
TO CHAPTER 6 337 7 APPLICATION TO HANKEL TYPE AND MULTIDIMENSIONAL
INTEGRAL EQUATIONS 339 34 CONVOLUTION INTEGRAL EQUATIONS OF HANKEL TYPE
339 34.1 FORMULATION OF THE MAIN RESULT 340 34.2 THE SCHEME OF THE PROOF
AND SOME BASIC IDEAS 343 34.3 PROOF OF THEOREM 34.1. THE CASE P = 2, 7 =
0 347 34.4 PROOF OF THEOREM 34.1. THE GENERAL CASE 349 34.5 THE CASE OF
THE EQUATION CORRESPONDING TO THE DIFFRACTION PROBLEM 359 35 SOME
MULTIDIMENSIONAL SINGULAR TYPE EQUATIONS WITH SHIFTS . . . 361 35.1 SOME
PROPERTIES OF LINEAR INVOLUTIVE TRANSFORMATIONS IN R N 361 35.2
WIENER-HOPF OPERATORS WITH REFLECTION IN SECTORS ON THE PLANE 366 35.3
CONVOLUTION OPERATORS WITH CARLEMAN LINEAR TRANSFORM . 370 35.4
EQUATIONS WITH HOMOGENEOUS KERNELS AND THE INVERSION SHIFT IN R N 379
35.5 FUNCTIONAL EQUATIONS WITH SHIFTS IN DIFFERENT VARIABLES . . 385
35.6 ON A FUNCTIONAL EQUATION ON THE TORUS AND FACTORIZATION WITH SHIFT
388 36 BIBLIOGRAPHIC NOTES TO CHAPTER 7 393 CONTENTS XIN BIBLIOGRAPHY
395 INDEX 419 LIST OF SYMBOLS 425
|
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| dewey-ones | 515 - Analysis |
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| id | DE-604.BV013953190 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:55:01Z |
| institution | BVB |
| isbn | 3764341572 0817641572 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009548950 |
| oclc_num | 46822470 |
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| owner | DE-824 DE-703 DE-91G DE-BY-TUM DE-11 |
| owner_facet | DE-824 DE-703 DE-91G DE-BY-TUM DE-11 |
| physical | XXII, 427 S. 24 cm |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Birkhäuser |
| record_format | marc |
| spelling | Karapetjanc, Nikolaj K. 1942- Verfasser (DE-588)123081963 aut Equations with involutive operators Nikolai Karapetiants ; Stefan Samko Boston [u.a.] Birkhäuser 2001 XXII, 427 S. 24 cm txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 395 - 418 Fredholm operators Integral equations Fredholm-Operator (DE-588)4155256-8 gnd rswk-swf Integralgleichung (DE-588)4027229-1 gnd rswk-swf Fredholm-Operator (DE-588)4155256-8 s Integralgleichung (DE-588)4027229-1 s DE-604 Samko, Stefan G. Verfasser aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009548950&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Karapetjanc, Nikolaj K. 1942- Samko, Stefan G. Equations with involutive operators Fredholm operators Integral equations Fredholm-Operator (DE-588)4155256-8 gnd Integralgleichung (DE-588)4027229-1 gnd |
| subject_GND | (DE-588)4155256-8 (DE-588)4027229-1 |
| title | Equations with involutive operators |
| title_auth | Equations with involutive operators |
| title_exact_search | Equations with involutive operators |
| title_full | Equations with involutive operators Nikolai Karapetiants ; Stefan Samko |
| title_fullStr | Equations with involutive operators Nikolai Karapetiants ; Stefan Samko |
| title_full_unstemmed | Equations with involutive operators Nikolai Karapetiants ; Stefan Samko |
| title_short | Equations with involutive operators |
| title_sort | equations with involutive operators |
| topic | Fredholm operators Integral equations Fredholm-Operator (DE-588)4155256-8 gnd Integralgleichung (DE-588)4027229-1 gnd |
| topic_facet | Fredholm operators Integral equations Fredholm-Operator Integralgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009548950&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT karapetjancnikolajk equationswithinvolutiveoperators AT samkostefang equationswithinvolutiveoperators |