Hypersingular integrals and their applications:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
London [u.a.]
Taylor & Francis
2002
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Analytical methods and special functions
5 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009955594&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XVII, 359 S. |
| ISBN: | 9780415272681 |
Internformat
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| 100 | 1 | |a Samko, Stefan G. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Hypersingular integrals and their applications |c Stefan G. Samko |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a London [u.a.] |b Taylor & Francis |c 2002 | |
| 300 | |a XVII, 359 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Analytical methods and special functions |v 5 | |
| 650 | 7 | |a Operadores (teoria) |2 larpcal | |
| 650 | 7 | |a Operadores integrais |2 larpcal | |
| 650 | 7 | |a Teoria do potencial |2 larpcal | |
| 650 | 4 | |a Singular integrals | |
| 650 | 0 | 7 | |a Singuläres Integral |0 (DE-588)4181533-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Singuläres Integral |0 (DE-588)4181533-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Analytical methods and special functions |v 5 |w (DE-604)BV011932737 |9 5 | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-009955594 | |
Datensatz im Suchindex
| _version_ | 1825759196644114432 |
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| adam_text |
HYPERSINGULAR INTEGRALS AND THEIR APPLICATIONS STEFAN G. SAMKO ROSTOV
STATE UNIVERSITY, RUSSIA AND UNIVERSITY OFALGARVE, PORTUGAL LONDON AND
NEW YORK CONTENTS PREFACE XV NOTATION 1 PART 1. HYPERSINGULAR INTEGRALS
3 CHAPTER 1. SOME BASICS FROM THE THEORY OF SPECIAL FUNCTIONS AND
OPERATOR THEORY 5 1. SOME SPECIAL FUNCTIONS 5 1.1. EULER GAMMA- AND
BETA-FUNCTIONS 5 1.2. ORTHOGONAL GEGENBAUER AND CHEBYSHEV POLYNOMIALS
C^(T), A 0, ANDT M (T) 7 1.3. BESSEL FUNCTIONS J V {Z) T I V (Z) AND K
V [Z) 8 1.4. THE GAUSS HYPERGEOMETRIC FUNCTION 9 2. BASICS OF THE THEORY
OF SPHERICAL HARMONICS 10 2.1. THE BASIS OF SPHERICAL HARMONICS 10 2.2.
THE ADDITION THEOREM AND THE FUNK-HEKKE FORMULA 12 2.3. THE CONNECTION
BETWEEN THE SMOOTHNESS OF A FUNCTION AND THE CONVERGENCE OF ITS
FOURIER-LAPLACE SERIES 14 3. ON FRACTIONAL INTEGRATION AND
DIFFERENTIATION OF FUNCTIONS OF ONE VARIABLE 16 4. FOURIER TRANSFORMS
AND THE WIENER RING; FOURIER MULTIPLIERS 18 4.1. THE WIENER RING 19 4.2.
FOURIER MULTIPLIERS 24 5. MISCELLANEOUS 24 5.1. ON ESTIMATION OF THE
TAYLOR REMAINDER FOR HOLDERIAN FUNCTIONS 24 5.2. ANALYTICITY OF
INTEGRALS DEPENDING ON A PARAMETER 25 5.3. ' HADAMARD'S APPROACH TO
DIVERGENT INTEGRALS AND THEIR REGULARIZATION 26 5.4. ESTIMATES OF SOME
MULTIDIMENSIONAL INTEGRALS 30 6. BIBLIOGRAPHICAL NOTES TO CHAPTER 1 34
CHAPTER 2. THE RIESZ POTENTIAL OPERATOR AND LIZORKIN TYPE INVARIANT
SPACES $V 37 1. THE RIESZ POTENTIAL OPERATOR 37 1.1. DEFINITIONS AND THE
FOURIER TRANSFORM OF THE RIESZ POTENTIAL IN THE CASE 0 3?A A^I 37
1.2. MAPPING PROPERTIES OF THE OPERATOR I A IN THE SPACES L P (R N ) AND
L P (R";P) 38 2. THE LIZORKIN SPACE $ 39 VIII CONTENTS 3. THE RIESZ
POTENTIAL IN THE GENERAL CASE 5FTA 0 AND INVARIANCE OF THE SPACE $ 43
3.1. THE FUNCTION L/\X\ A AS A DISTRIBUTION IN S'(R N ) OR $'(R N ) 43
3.2. THE FOURIER TRANSFORM OF THE DISTRIBUTION L/|SC| A 44 3.3. THE
RIESZ KERNEL AND THE RIESZ POTENTIAL IN THE GENERAL CASE 45 4.
LIZORKIN-TYPE SPACES $V 46 4.1. DEFINITIONS, EXAMPLES AND SIMPLE
PROPERTIES 46 4.2. DENSENESS OF *V AND $Y IN L P (R N ) 50 5.
CONNECTIONS OF THE RIESZ POTENTIAL WITH THE POISSON AND
GAUSS-WEIERSTRASS SEMIGROUPS OF OPERATORS 53 6. BIBLIOGRAPHICAL NOTES TO
CHAPTER 2 54 CHAPTER 3. HYPERSINGULAR INTEGRALS WITH CONSTANT
CHARACTERISTICS 55 1. THE RIESZ FRACTIONAL DIFFERENTIATION W 56 1.1.
FOURIER TRANSFORM OF THE HYPERSINGULAR INTEGRAL W F 57 1.2. ZEROS OF THE
FUNCTION D NI I(A) 58 1.3. THE PHENOMENON OF ANNIHILATION OF
HYPERSINGULAR INTEGRALS 61 1.4. CONVERGENCE OF THE HYPERSINGULAR
INTEGRAL W F IN THE CASE OF SMOOTH FUNCTIONS; MOMENTS OF HYPERSINGULAR
INTEGRALS 62 1.5. DIMINUTION OF ORDER I SFTA TO I 2 [^P] IN THE CASE
OF A NON-CENTRED DIFFERENCE 64 2. THE HYPERSINGULAR OPERATOR W AS
INVERSE TO THE RIESZ POTENTIAL OPERATOR I A 65 2.1. AUXILIARY FUNCTIONS
AI IO ,(X,H), KI (X) AND * |FL ,(|X|) 65 2.2. THE INVERSION THEOREM 70
2.3. ALMOST EVERYWHERE CONVERGENCE OF THE RIESZ DERIVATIVE 71 2.4.
REDUCING THE ORDER A: THE CASE OF COMPLEX A 73 3. MORE ON THE
INDEPENDENCE OF W F ON THE ORDER OF FINITE DIFFERENCES 73 4. A ZYGMUND
TYPE ESTIMATE FOR THE CONTINUITY MODULUS OF HYPERSINGULAR INTEGRALS 75
5. CONNECTION OF HYPERSINGULAR INTEGRALS WITH FRACTIONAL POWERS OF
OPERATORS 76 6. HYPERSINGULAR INTEGRALS WITH GENERALIZED DIFFERENCES 78
6.1. GENERALIZED DIFFERENCES 78 6.2. MODIFIED HYPERSINGULAR INTEGRALS
AND THEIR FOURIER TRANSFORMS 80 6.3. PROPERTIES OF THE FUNCTION AT{A) 81
6.4. MODIFIED HYPERSINGULAR INTEGRAL AS INVERSE TO THE RIESZ POTENTIAL
OPERATOR 83 7. BIBLIOGRAPHICAL NOTES TO CHAPTER 3 84 CHAPTER 4.
POTENTIALS AND HYPERSINGULAR INTEGRALS WITH HOMOGENEOUS CHARACTE-
RISTICS 87 1. PRELIMINARIES ON SOME MEANS OF FUNCTIONS ON THE UNIT
SPHERE IN R N 87 1.1. SOME MEANS OF FUNCTIONS ON THE UNIT SPHERE 87 1.2.
ON THE CHOICE OF A ROTATION WHICH IS SMOOTH WITH RESPECT TO THE
PARAMETER 89 1.3. ON SMOOTHNESS OF THE MEANS M U ,(X',T) 90 1.4.
CAVALIERI TYPE PRINCIPLE AND THE MEANS OF SPHERICAL HARMONICS 93 2.
POTENTIAL TYPE OPERATORS WITH HOMOGENEOUS CHARACTERISTICS 94 2.1. THE
SYMBOL IN THE CASE 0 3TA 1 95 CONTENTS IX 2.2. THE HADAMARD
CONSTRUCTIONS OF DIVERGENT INTEGRALS OVER THE SPHERE IN THE CASE OF
SINGULARITY AT AN EQUATOR 95 2.3. ON THE SYMBOL K^{X) IN THE CASE 3TA
1 99 2.4. SMOOTHNESS PROPERTIES OF THE SYMBOL IC"(X) 100 2.5. ON THE
INVERSION OF THE OPERATOR "CHARACTERISTIC * SYMBOL" 102 3.
HYPERSINGULAR INTEGRALS WITH HOMOGENEOUS CHARACTERISTICS 103 3.1.
CLASSIFICATION OF HYPERSINGULAR INTEGRALS 104 3.2. SYMBOL OF A
HYPERSINGULAR INTEGRAL 106 3.3. A HYPERSINGULAR INTEGRAL AS A
CONVOLUTION WITH THE FUNCTION |"IWIFL 108 3.4. SYMBOL OF A HYPERSINGULAR
OPERATOR AS THE FOURIER TRANSFORM OF A DISTRIBUTION 110 3.5. SOME
ESTIMATES OF HYPERSINGULAR INTEGRALS OF SMOOTH FUNCTIONS VANISHING AT
INFINITY 112 3.6. SMOOTHNESS PROPERTIES OF THE SYMBOL X ^(X) 113 4.
REPRESENTATION OF HOMOGENEOUS DIFFERENTIAL OPERATORS IN PARTIAL
DERIVATIVES BY MEANS OF HYPERSINGULAR OPERATORS 114 4.1. HYPERSINGULAR
INTEGRALS WITH HARMONIC CHARACTERISTICS 114 4.2. ON A CERTAIN INTEGRAL
EQUATION OF THE FIRST KIND ON THE UNIT SPHERE: THE CASE OF A NON-INTEGER
A 116 4.3. THE CASE OF INTEGER A AND THE MAIN REPRESENTATION THEOREM 118
5. BIBLIOGRAPHICAL NOTES TO CHAPTER 4 120 CHAPTER 5. HYPERSINGULAR
INTEGRALS WITH NON-HOMOGENEOUS CHARACTERISTICS 121 1. ON THE CONNECTION
WFT IC F = AJD?F 121 2. THE LIMITING OPERATOR A = LIRRIE-VO A E AND
JUSTIFICATION OF THE CONVERGENCE 127 2.1. INTEGRABILITY OF THE KERNEL
A(X) AND ITS FOURIER TRANSFORM 127 2.2. JUSTIFICATION OF THE CONVERGENCE
A E * A AS E * 0 129 3. THE MAIN THEOREMS ON THE CONVERGENCE OF E3^
E F 132 4. REPRESENTATION OF A HYPERSINGULAR INTEGRAL AS A CONVOLUTION
WITH A FUNCTION OF THE TYPE . AY O AND THE INVERSE PROBLEM 133 4.1. ON A
/.P.-CONVOLUTION 134 4.2. REPRESENTATION OF A HYPERSINGULAR INTEGRAL AS
A /.P.-CONVOLUTION 134 4.3. ON A FUNCTIONAL EQUATION 136 4.4. ON THE
INVERSE PROBLEM 139 5. ON THE CONTINUITY MODULUS OF A HYPERSINGULAR
INTEGRAL 143 6. BIBLIOGRAPHICAL NOTES TO CHAPTER 5 143 CHAPTER 6.
HYPERSINGULAR INTEGRALS ON THE UNIT SPHERE 145 1. SPHERICAL CONVOLUTION
OPERATORS. OPERATORS COMMUTING WITH ROTATIONS 145 1.1. SPHERICAL
CONVOLUTION OPERATORS ON HARMONICS 145 1.2. OPERATORS COMMUTING WITH
ROTATIONS 147 1.3. GENERALIZED FUNCTIONS (DISTRIBUTIONS) ON THE SPHERE
149 1.4. BOUNDEDNESS OF CONVOLUTION OPERATORS IN L P (S N ~ 1 ) 149 2.
SPHERICAL POTENTIALS 150 2.1. THE SPHERICAL RIESZ POTENTIAL OPERATOR 151
2.2. CONNECTION WITH THE SPATIAL RIESZ POTENTIAL 153 2.3. OTHER
POTENTIALS 153 3. SPHERICAL HYPERSINGULAR INTEGRALS AND INVERSION OF THE
SPHERICAL RIESZ POTENTIAL 159 X CONTENTS 3.1. SPHERICAL HYPERSINGULAR
INTEGRALS OF ORDER 0 3TA 2 159 3.2. THE MULTIPLIER OF THE SPHERICAL
HYPERSINGULAR OPERATOR 160 3.3. JUSTIFICATION OF THE INVERSION IN Z^S" 1
" 1 ); IDENTITY APPROXIMATION ON THE SPHERE 160 3.4. INVERSION OF THE
SPHERICAL RIESZ POTENTIAL IN THE CASE 3TA 2 165 4. ZYGMUND TYPE
ESTIMATES FOR SPHERICAL POTENTIAL OPERATORS AND SPHERICAL HYPERSINGULAR
INTEGRALS 167 4.1. THE CONTINUITY MODULUS OF FUNCTIONS ON THE SPHERE 167
4.2. TECHNICAL LEMMA 167 4.3. THE CASE OF POTENTIALS 168 4.4. THE CASE
OF HYPERSINGULAR INTEGRALS 170 5. BIBLIOGRAPHICAL NOTES TO CHAPTER 6 170
PART 2. APPLICATIONS OF HYPERSINGULAR INTEGRALS 173 CHAPTER 7.
CHARACTERIZATION OF SOME FUNCTION SPACES IN TERMS OF HYPERSINGULAR
INTEGRALS 175 1. THE SPACES I A (L P ) OF RIESZ POTENTIALS 175 1.1.
DEFINITIONS AND LOCAL BEHAVIOUR OF RIESZ POTENTIALS 175 1.2.
CHARACTERIZATION OF THE SPACE, I A (L P ) IN TERMS OF CONVERGENCE OF
HYPERSINGULAR INTEGRALS 179 2. THE SPACES B A (L P ) OF BESSEL
POTENTIALS 184 2.1. DENSENESS OF CFI(R N ) IN THE SPACE L^(R N ) 185
2.2. PROOF OF THE MAIN RESULT B *(L P ) = L^{R") 186 3. THE SPACES L^ R
(R N ) 187 R 3.1. CONNECTION WITH THE SPACE OF RIESZ POTENTIALS 188 3.2.
IMBEDDINGS IN THE SPACES L^ R (R N ) 189 3.3. WEAK DERIVATIVES OF
FUNCTIONS FEL^ R (R N ) 190 3.4. RIESZ DERIVATIVES W*F OF INTEGER ORDER
AND POWERS OF THE LAPLACE OPERATOR, FEI A {L P ) 192 3.5. THE SPACES WJF
R AND THE CHARACTERIZATION OF THE SPACE I A (L P ) IN TERMS OF HIGHER
DERIVATIVES 192 3.6. SPACES L PR (P P ,P R ) WITH MUCKENHOUPT WEIGHT
FUNCTIONS 193 4. SIMULTANEOUS APPROXIMATION OF FUNCTIONS AND THEIR RIESZ
DERIVATIVES IN DIFFERENT L P -NORMS 196 5. CONVERGENCE IN L P OF
HYPERSINGULAR INTEGRALS WITH NON-STABILIZING CHARAC- TERISTICS 204 6.
HYPERSINGULAR INTEGRALS AND DIFFERENCES OF FRACTIONAL ORDER 207 6.1.
FRACTIONAL DIFFERENTIATION IN A GIVEN DIRECTION 208 6.2. THE CASE OF
ORDINARY FRACTIONAL DIFFERENCES 209 6.3. THE CASE OF MIXED FRACTIONAL
DIFFERENCES 213 6.4. THE CASE OF OPERATOR FRACTIONAL DIFFERENCE 214 6.5.
UNIFORM ESTIMATES 216 7. SPACES OF RIESZ POTENTIALS WITH DENSITIES IN
ORLICZ SPACES 220 7.1. DEFINITIONS 221 7.2. ON BOUNDEDNESS OF THE RIESZ
POTENTIAL OPERATOR IN ORLICZ SPACES 221 7.3. THE SPACE I A (E M ) OF
RIESZ POTENTIALS 222 7.4. THE SPACES E^^RT) 222 8. CHARACTERIZATION OF
THE SPACES L"(5 N ~ 1 ) 223 CONTENTS 8.1. CHARACTERIZATION OF THE RANGE
. A (L P ) 223 8.2. PROOF OF THE COINCIDENCE & A {L P ) = L^S"" 1 ) 225
9. BIBLIOGRAPHICAL NOTES TO CHAPTER 7 226 CHAPTER 8. SOLUTION OF
MULTIDIMENSIONAL INTEGRAL EQUATIONS OF THE FIRST KIND WITH A POTENTIAL
TYPE KERNEL 231 1. INVERSION OF POTENTIAL TYPE OPERATORS WITH
HOMOGENEOUS CHARACTERISTICS IN THE ELLIPTIC CASE 231 1.1. GENERAL
REMARKS ON THE INVERSION 231 1.2. STRUCTURE OF THE FOURIER TRANSFORM OF
THE RECIPROCAL OF THE SYMBOL OF A POTENTIAL 232 1.3. REPRESENTATION OF
F~ X (*%?) BY AN F.P.-INTEGRAL OVER THE SPHERE 233 1.4. THE ASSOCIATED
CHARACTERISTICS 234 1.5. INVERSION OF POTENTIALS OF NON-INTEGER ORDER A
BY HYPERSINGULAR OPERA- TORS 236 1.6. INVERSION OF POTENTIALS OF EVEN
ORDER A = 2,4,6,. BY HYPERSINGULAR OPERATORS 237 1.7. INVERSION OF
POTENTIALS OF ODD ORDER A = 1,3,5,. BY HYPERSINGULAR OPERATORS 238
1.8. ON THE INVERSION OF POTENTIALS OF INTEGER ORDER IN THE GENERAL CASE
239 2. EXTENSION TO THE CASE OF DENSITIES IN L P (R N ) 241 2.1. THE
ANNIHILATION OF THE KERNEL OF A POTENTIAL BY THE ASSOCIATED HYPER- '
SINGULAR OPERATOR 242 2.2. FUNDAMENTAL SOLUTIONS OF HYPERSINGULAR
OPERATORS 244 2.3. INTEGRAL REPRESENTATION OF TRUNCATED HYPERSINGULAR
INTEGRALS 245 2.4. THE FOURIER TRANSFORM OF THE KERNEL OF THE
REPRESENTATION 246 2.5. THE KERNEL OF THE REPRESENTATION AS AN IDENTITY
APPROXIMATION KERNEL IN THE CASE OF ASSOCIATED CHARACTERISTICS 247 2.6.
CONVERGENCE IN L P OF THE TRUNCATED HYPERSINGULAR INTEGRALS AND
INVERSION OF POTENTIALS WITHIN THE FRAMEWORK OF L P -SPACES 248 3.
INVERSION OF POTENTIALS WITH HOMOGENEOUS HARMONIC CHARACTERISTICS 249
3.1. THE GENERAL CASE 250 3.2. THE CASE OF A LINEAR CHARACTERISTIC 251
3.3. REALIZATION OF THE INVERSION FOR DENSITIES IN L P (R N ) IN THE
CASE OF A LINEAR CHARACTERISTIC 253 4. INVERSION OF POTENTIALS WITH
HOMOGENEOUS CHARACTERISTICS IN THE CASE OF LINEAR DEGENERACY OF THE
SYMBOL 257 4.1. CHARACTERISTICS OF POTENTIALS WITH A LINEAR DEGENERACY
OF THE SYMBOL 257 4.2. INVERSION IN THE CASE OF "NICE" FUNCTIONS 257
4.3. THE INVERSION IN THE CASE OF FUNCTIONS (P * L P 258 5. INVERSION OF
POTENTIALS WITH RADIAL DIFFERENCE CHARACTERISTICS 260 . 5.1. WHAT IS TO
BE DONE? 260 5.2. THE CLASS C M "{R\) 261 5.3. ON A HANKEL
TRANSFORMATION 263 5.4. THE ANALYTICAL CONTINUATION OF THE FOURIER
TRANSFORM OF THE FUNCTION |Z| A (L + |:C| 2 )-* 264 5.5. CONSTRUCTION OF
THE INVERSE OPERATOR 265 XII CONTENTS 5.6. HYPERSINGULAR INTEGRALS AS
INVERSES: THE CASES 0 A 1 AND 1 A 2 267 5.7. JUSTIFICATION OF THE
INVERSION IN THE LIZORKIN SPACE $(I? N ) 267 5.8. JUSTIFICATION OF THE
INVERSION IN THE SPACE L P : THE CASES 0 A 1 AND 1 A 2 268 6.
BIBLIOGRAPHICAL NOTES TO CHAPTER 8 269 CHAPTER 9. HYPERSINGULAR
OPERATORS AS POSITIVE FRACTIONAL POWERS OF SOME OPERATORS OF
MATHEMATICAL PHYSICS 271 1. INVERSION OF THE BESSEL POTENTIALS 271 1.1.
THE IDEA OF THE CONSTRUCTION 271 1.2. PROPERTIES OF THE FUNCTION W_ A
(R) 272 1.3. THE OPERATOR (/ * A)"/ 2 INVERSE TO THE BESSEL POTENTIAL
OPERATOR 274 1.4. JUSTIFICATION OF THE INVERSION IN THE CASE OF "NICE"
FUNCTIONS 276 1.5. THE CASE 0 3?A 2 276 1.6. JUSTIFICATION OF THE
INVERSION IN L P : THE CASES 0 3?A 1 AND 1 SO 2 278 1.7. ANOTHER
FORM FOR (/-A) 01 / 2 279 1.8. ANOTHER EXPRESSION FOR (/ - A)"/ 2 281 2.
PARABOLIC (HEAT) HYPERSINGULAR INTEGRALS 282 2.1. PARABOLIC FRACTIONAL
POTENTIALS 282 2.2. POSITIVE FRACTIONAL POWERS (JJ - A X )" /2 AND (/ +
- A X )" /2 , A 0 284 2.3. JUSTIFICATION OF THE INVERSION IN THE
CASE OF "NICE" FUNCTIONS 286 2.4. THE CASE OF FUNCTIONS IN L P 288 2.5.
THE SPACES OF PARABOLIC POTENTIALS 288 3. FRACTIONAL POWERS OF THE
HYPERBOLIC (WAVE) OPERATOR 290 3.1. THE RIESZ HYPERBOLIC POTENTIAL IN
THE CASE N = 2 291 3:2. THE HYPERBOLIC HYPERSINGULAR INTEGRAL: THE CASE
N = 2 292 3.3. HYPERBOLIC HYPERSINGULAR INTEGRALS: THE GENERAL CASE N
2 294 4. FRACTIONAL POWERS OF THE SCHRODINGER OPERATOR 296 4.1. THE
FRACTIONAL SCHRODINGER POTENTIAL OPERATOR 296 4.2. ANALYTICAL
CONTINUATION OF THE SCHRODINGER FRACTIONAL POTENTIAL 297 4.3. POSITIVE
FRACTIONAL POWERS OF THE SCHRODINGER OPERATOR 299 5. FRACTIONAL POWERS
OF SOME OTHER DIFFERENTIAL OPERATORS 300 6. BIBLIOGRAPHICAL NOTES TO
CHAPTER 9 302 CHAPTER 10. REGULARIZATION OF MULTIDIMENSIONAL INTEGRAL
EQUATIONS OF THE FIRST KIND WITH A POTENTIAL TYPE KERNEL 303 1.
REGULARIZATION OF THE EQUATIONS IN IT" 303 1.1. THE CASE 0 A 1 304
1.2. THE CASE O 1 309 2. APPLICATION OF SPHERICAL HYPERSINGULAR
OPERATORS TO REGULARIZATION OF INTEGRAL EQUATIONS OF THE FIRST KIND ON
THE UNIT SPHERE 310 3. BIBLIOGRAPHICAL NOTES TO CHAPTER 10 314 CHAPTER
11. SOME MODIFICATIONS OF HYPERSINGULAR INTEGRALS AND THEIR APPLICA-
TIONS 315 1. THE CASE OF THE RIESZ POTENTIAL OPERATOR 316 CONTENTS XIII
1.1. GENERAL REQUIREMENTS FOR THE KERNEL Q A (Y) 316 1.2. CONVERGENCE IN
(11.4) ON "NICE" FUNCTIONS 318 1.3. CONSTRUCTION (11.4) AS THE INVERSE
OPERATOR TO I A ON I"(L P ) 318 1.4. THE APPROXIMATIVE INVERSE OPERATOR
UNDER THE CHOICE K(X) = P(X, 1) 319 1.5. THE APPROXIMATIVE INVERSE
OPERATOR UNDER THE DIRECT CHOICE OF Q A (X) 321 2. INVERSION OF
POTENTIAL TYPE OPERATORS WITH HOMOGENEOUS CHARACTERISTICS BY
APPROXIMATIVE INVERSES 325 2.1. GENERAL REQUIREMENTS FOR THE KERNEL Q A
{X) IN (11.4) 326 2.2. APPROXIMATIVE INVERSES UNDER THE CHOICE K{) = E~
^ 326 2.3. INVERSION IN THE NON-ELLIPTIC CASE 327 3. INVERSION OF BESSEL
POTENTIALS BY APPROXIMATIVE INVERSES 329 3.1. APPROXIMATIVE INVERSES
UNDER THE CHOICE IC E () = E~ E ^ 329 3.2. THE APPROXIMATIVE INVERSES
UNDER THE CHOICE E () = * A 330 4. INVERSION OF THE ACOUSTIC
POTENTIALS BY APPROXIMATIVE INVERSES 331 4.1. SOME PRELIMINARIES 331
4.2. THE CHOICE OF APPROXIMATIVE INVERSES 333 4.3. THE REPRESENTATION
FOR (A A )~ 1 A A ,C 0 333 4.4. THE INVERSION THEOREM 335 5. INVERSION
OF POTENTIALS WITH OSCILLATING SYMBOLS BY APPROXIMATIVE INVERSES 336
5.1. THE KERNEL CORRESPONDING TO THE OSCILLATING SYMBOL B AI -Y() 336
5.2. PASSAGE TO THE SYMBOL 337 5.3. THE INVERSION 338 6. OTHER
APPLICATIONS OF THE APPROXIMATIVE INVERSES METHOD 339 7. BIBLIOGRAPHICAL
NOTES TO CHAPTER 11 340 REFERENCES 343 AUTHOR INDEX 355 SUBJECT INDEX
357 INDEX OF SYMBOLS 359 |
| any_adam_object | 1 |
| author | Samko, Stefan G. |
| author_facet | Samko, Stefan G. |
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| callnumber-sort | QA 3311 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 450 |
| ctrlnum | (OCoLC)50783759 (DE-599)BVBBV014674163 |
| dewey-full | 515.723 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.723 |
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| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV014674163 |
| illustrated | Not Illustrated |
| indexdate | 2025-03-05T13:00:53Z |
| institution | BVB |
| isbn | 9780415272681 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009955594 |
| oclc_num | 50783759 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-83 |
| owner_facet | DE-355 DE-BY-UBR DE-83 |
| physical | XVII, 359 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Taylor & Francis |
| record_format | marc |
| series | Analytical methods and special functions |
| series2 | Analytical methods and special functions |
| spelling | Samko, Stefan G. Verfasser aut Hypersingular integrals and their applications Stefan G. Samko 1. publ. London [u.a.] Taylor & Francis 2002 XVII, 359 S. txt rdacontent n rdamedia nc rdacarrier Analytical methods and special functions 5 Operadores (teoria) larpcal Operadores integrais larpcal Teoria do potencial larpcal Singular integrals Singuläres Integral (DE-588)4181533-6 gnd rswk-swf Singuläres Integral (DE-588)4181533-6 s DE-604 Analytical methods and special functions 5 (DE-604)BV011932737 5 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009955594&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Samko, Stefan G. Hypersingular integrals and their applications Analytical methods and special functions Operadores (teoria) larpcal Operadores integrais larpcal Teoria do potencial larpcal Singular integrals Singuläres Integral (DE-588)4181533-6 gnd |
| subject_GND | (DE-588)4181533-6 |
| title | Hypersingular integrals and their applications |
| title_auth | Hypersingular integrals and their applications |
| title_exact_search | Hypersingular integrals and their applications |
| title_full | Hypersingular integrals and their applications Stefan G. Samko |
| title_fullStr | Hypersingular integrals and their applications Stefan G. Samko |
| title_full_unstemmed | Hypersingular integrals and their applications Stefan G. Samko |
| title_short | Hypersingular integrals and their applications |
| title_sort | hypersingular integrals and their applications |
| topic | Operadores (teoria) larpcal Operadores integrais larpcal Teoria do potencial larpcal Singular integrals Singuläres Integral (DE-588)4181533-6 gnd |
| topic_facet | Operadores (teoria) Operadores integrais Teoria do potencial Singular integrals Singuläres Integral |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009955594&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011932737 |
| work_keys_str_mv | AT samkostefang hypersingularintegralsandtheirapplications |