Fractional integrals and potentials:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Harlow
Longman
1996
|
| Edition: | 1. publ. |
| Series: | Pitman monographs and surveys in pure and applied mathematics
82 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 409 S. |
| ISBN: | 0582253411 |
Staff View
MARC
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| 100 | 1 | |a Rubin, Boris |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Fractional integrals and potentials |c Boris Rubin |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Harlow |b Longman |c 1996 | |
| 300 | |a XIV, 409 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pitman monographs and surveys in pure and applied mathematics |v 82 | |
| 650 | 7 | |a Funções integrais |2 larpcal | |
| 650 | 4 | |a Fractional calculus | |
| 650 | 4 | |a Functions | |
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Record in the Search Index
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| adam_text | Contents
Preface xi
Notation xiii
Chapter 1 Generalities
1. Auxiliary facts 1
2. The Fourier analysis 6
2.1. The Fourier transform on Rn and multipliers 6
2.2. Spherical harmonics and related topics 9
3. Distributions 13
3.1. The space 5 of test functions 13
3.2. The space S of tempered distributions 14
3.3. Spaces $y of the Lizorkin type 19
Chapter 2 One dimensional fractional integrals
4. Some basic facts related to fractional integrals 23
4.1. Definitions and simplest properties 23
4.2. The Fourier transform of fractional integrals 32
4.3. The Mellin transform and multipliers 42
4.4. Integrals of the potential type 48
4.5. Action on Lp and Holder spaces 59
5. Relations between fractional and singular integrals 61
5.1. One sided fractional integrals and singular operators 62
5.1.1. The case of a finite interval 62
5.1.2. The case of a half line 68
5.1.3. The case of the whole real line 71
5.2. On the ranges of fractional integrals and Riesz potentials 72
6. Restriction and extension 78
6.1. Restriction problems 78
6.2. Extension problems 84
6.3. Multiplication by a characteristic function and additivity 90
7. Local properties of fractional integrals and a limit exponent 95
viii CONTENTS
7.1. Estimates of local characteristics 96
7.2. Fractional integrals with a limit exponent (the BMO approach) 102
7.3. Spaces defined by asymptotics of the L9 norm, q — oo 108
7.4. Spaces Ky,A,M(0,1) of local type 111
7.5. On the relation between left sided and right sided fractional integrals 116
8. Action on weighted Lp and Holder spaces 117
8.1. Preliminaries 117
8.2. Estimates of Lp L« type 121
8.2.1. The case of the weight at one point 121
8.2.2. Estimates on a finite interval 122
8.2.3. Estimates on infinite intervals 123
8.3. Estimates of L? #a_1/p type 125
8.4. Estimates of #M ffM+Q type 130
9. Fractional integrals of generalized functions 133
9.1. Fractional integrals on the real line 133
9.2. Fractional integrals on a half line 138
9.2.1. Spaces of test functions 139
9.2.2. Fractional integrals on the spaces of test functions
and on the spaces of distributions 143
9.2.3. Some generalizations 144
10. The Marchaud method 145
10.1. Generalized finite differences 146
10.2. Analytic continuation of integrals of functions
with a power singularity 149
10.3. Marchaud s fractional derivatives of functions from the
Lizorkin space 157
10.4. The case of more general function spaces 161
10.5. Inversion of fractional integrals of finite measures 165
10.6. Fractional integrals of purely imaginary order 167
10.7. A generalization of Marchaud s method 169
11. Regularized solutions to Abel s integral equation 170
11.1. Regularized inversion of fractional integrals on the real line 172
11.2. Fractional integrals of Borel measures 175
11.2.1. The first approach 176
11.2.2. The second approach 178
11.3. Regularization on a finite interval 181
CONTENTS ix
Chapter 3 Fractional integro differentiation via wavelet transforms
12. On the Calderon reproducing formula 186
13. Integrals/Q(/i,/). Representation of fractional derivatives 194
13.1. Preliminaries 194
13.1.1. The case Rea 0 195
13.1.2. The case Rea = 0 201
13.2. Lp theorems 205
13.3. Some generalizations 209
14. Representation of fractional integrals 210
Chapter 4 Riesz potentials on En
15. Preliminaries 215
16. Inversion by means of the Poisson and the Gauss Weierstrass integrals 217
16.1. Riesz potentials and Poisson integrals 217
16.2. Riesz potentials and Gauss Weierstrass integrals 222
17. Wavelet type representation of the Riesz fractional derivative 224
17.1. Auxiliary functions 225
17.2. Truncated integrals 229
17.3. Inversion of Riesz potentials with Lp densities 235
17.4. Examples 237
18. Multiplication by the characteristic function of the Strichartz domain 242
Chapter 5 Oscillatory potentials on W1
19. The Helmholtz potentials 245
19.1. Potentials with a smooth density 246
19.2. Potentials with Lp density 253
20. Inversion of Bessel potentials by using continuation to R++1 257
20.1. On methaharmonk continuation of functions 257
20.2. Inversion of Bessel potentials by using a methaharmonic
continuation 258
20.3. Bessel potentials and Gauss Weierstrass integrals 262
Chapter 6 Potentials on a half space
21. One sided Riesz potentials 263
21.1. Definitions and basic properties 263
21.2. Inversion of one sided potentials 269
x CONTENTS
21.3. Restriction and extension 275
21.4. Factorization formula and relations between potentials 287
21.5. Inversion of Riesz potentials on a half space 294
22. One sided oscillatory potentials 295
22.1. Kernels of the Poisson type 296
22.2. Some properties of one sided oscillatory potentials 300
22.3. Inversion of one sided oscillatory potentials 309
22.4. Restriction and extension 313
22.5. Factorization and further properties 318
22.6. Inversion of oscillatory potentials on a half space 321
Chapter 7 Riesz potentials on a ball
23. Preliminaries. The radial spherical Fourier transform 324
24. The ball fractional integrals 328
25. Inversion of the ball fractional integrals 334
25.1. Inverting constructions 334
25.2. Inversion of S±v? in weighted Lp spaces 335
25.3. The case a 1 339
25.4. Inversion of B?± f 340
26. Traces on spherical surfaces 342
27. The restriction problem and inversion of Riesz potentials 349
Chapter 8 Fractional integrals on a sphere
28. Preliminaries 356
29. Inversion of Riesz potentials (a direct regularization) 360
30. Inversion of logarithmic potentials 365
31. Inversion of Riesz potentials by means of the Poisson integral 368
32. Spaces of fractional smoothness 372
33. Integral equations with a power logarithmic kernel 378
34. A spherical wavelet transform and a reproducing formula 382
Appendix 1 387
Appendix 2 390
Appendix 3 392
Bibliography 397
|
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| ctrlnum | (OCoLC)35137270 (DE-599)BVBBV011076735 |
| dewey-full | 515.83 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.83 |
| dewey-search | 515.83 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
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| id | DE-604.BV011076735 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:03:37Z |
| institution | BVB |
| isbn | 0582253411 |
| language | English |
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| physical | XIV, 409 S. |
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| publisher | Longman |
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| series | Pitman monographs and surveys in pure and applied mathematics |
| series2 | Pitman monographs and surveys in pure and applied mathematics |
| spelling | Rubin, Boris Verfasser aut Fractional integrals and potentials Boris Rubin 1. publ. Harlow Longman 1996 XIV, 409 S. txt rdacontent n rdamedia nc rdacarrier Pitman monographs and surveys in pure and applied mathematics 82 Funções integrais larpcal Fractional calculus Functions Integralgleichung (DE-588)4027229-1 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Integral gebrochener Ordnung (DE-588)4365957-3 gnd rswk-swf Integral gebrochener Ordnung (DE-588)4365957-3 s Integralgleichung (DE-588)4027229-1 s Harmonische Analyse (DE-588)4023453-8 s DE-604 Pitman monographs and surveys in pure and applied mathematics 82 (DE-604)BV000022446 82 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007420433&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rubin, Boris Fractional integrals and potentials Pitman monographs and surveys in pure and applied mathematics Funções integrais larpcal Fractional calculus Functions Integralgleichung (DE-588)4027229-1 gnd Harmonische Analyse (DE-588)4023453-8 gnd Integral gebrochener Ordnung (DE-588)4365957-3 gnd |
| subject_GND | (DE-588)4027229-1 (DE-588)4023453-8 (DE-588)4365957-3 |
| title | Fractional integrals and potentials |
| title_auth | Fractional integrals and potentials |
| title_exact_search | Fractional integrals and potentials |
| title_full | Fractional integrals and potentials Boris Rubin |
| title_fullStr | Fractional integrals and potentials Boris Rubin |
| title_full_unstemmed | Fractional integrals and potentials Boris Rubin |
| title_short | Fractional integrals and potentials |
| title_sort | fractional integrals and potentials |
| topic | Funções integrais larpcal Fractional calculus Functions Integralgleichung (DE-588)4027229-1 gnd Harmonische Analyse (DE-588)4023453-8 gnd Integral gebrochener Ordnung (DE-588)4365957-3 gnd |
| topic_facet | Funções integrais Fractional calculus Functions Integralgleichung Harmonische Analyse Integral gebrochener Ordnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007420433&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000022446 |
| work_keys_str_mv | AT rubinboris fractionalintegralsandpotentials |