Multidimensional singular integrals and integral equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Pergamon Press
1965
|
| Edition: | 1. Engl. ed. |
| Series: | International series of monographs in pure and applied mathematics
83 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus. dem Russ. übers. |
| Physical Description: | XII, 255 S. |
Staff View
MARC
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| 100 | 1 | |a Michlin, Solomon G. |d 1908-1990 |e Verfasser |0 (DE-588)172258243 |4 aut | |
| 240 | 1 | 0 | |a Mnogomernye singuljarnye integraly i integral'ny uravnenija |
| 245 | 1 | 0 | |a Multidimensional singular integrals and integral equations |c by S. G. Mikhlin |
| 250 | |a 1. Engl. ed. | ||
| 264 | 1 | |a Oxford [u.a.] |b Pergamon Press |c 1965 | |
| 300 | |a XII, 255 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a International series of monographs in pure and applied mathematics |v 83 | |
| 500 | |a Aus. dem Russ. übers. | ||
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Record in the Search Index
| _version_ | 1804135986249072640 |
|---|---|
| adam_text | CONTENTS
PREFACE xi
I. INTRODUCTION 1
§ 1. Review of previous work 1
§ 2. Some theorems on linear equations in Banaeh spaces 21
§ 3. Stereographic projection 30
§ 4. Completely continuous operators 32
H. SIMPLEST PROPERTIES OF MULTIDIMENSIONAL SINGULAR
INTEGRALS 37
§ 6. Basic concepts 37
§ 6. Lipschitz conditions 46
§ 7. Order of singular integrals at infinity 50
§ 8. Differentiation of integrals with a weak singularity 59
HI.. COMPOUNDING OF SINGULAR INTEGRALS 63
§ 9. Compounding of singular and ordinary integrals 63
§ 10. Compounding of double singular integrals 67
§ 11. The concept of a singular operator 70
§ 12. Compounding of double singular integrals. The symbol 71
§ 13. Compounding of multidimensional singular integrals 72
§ 14. Formulae for reference 74
§ 15. Product of the operators A1 and An 77
§ 16. Product of the operators A% and An 81
§ 17. Calculation of nlm 83
§ 18. Symbol of a multidimensional singular integral 86
IV. PROPERTIES OF THE SYMBOL 93
§ 19. Fourier transform of a singular kernel 93
§ 20. Fourier transform of a kernel and the symbol of a singular
operator 97
§ 21. Transformation of the symbol under change of variables 104
vii
viii CONTENTS
§ 22. Differentiability of the symbol 109
§ 23. The conditions for the continuity of the symbol 112
V. SINGULAR INTEGRALS IN Lp SPACES 116
§ 24. The simplest corollaries from the Fourier transform. First
theorem on boundedness in L2 space 116
§ 25. Symbol dependent on the pole. Second theorem on bounded
ness in £2 space 119
§ 26. On the boundedness of a singular integral operator in Lp
space 123
§ 27. Integrals taken over any manifold 130
§ 28. Differential properties of singular integrals 131
VI. FURTHER INVESTIGATION OF THE SYMBOL 134
§ 29. More about the differentiation of integrals with a weak
singularity 134
§ 30. Polyharmonic potentials 135
§ 31. Series of spherical functions 136
§ 32. Differential properties of the symbol and the characteristic 148
§ 33. Rule for the multiplication of the symbols in the general case 150
§ 34. Conjugate singular operator 154
VII. SINGULAR INTEGRAL EQUATIONS 157
§ 35. The case where the symbol is independent of the pole 157
§ 36. The case where the symbol is dependent on pole. Regulariza
tion and domains of constancy of the index 158
§ 37. Equivalent regularization. Index theorem 160
§ 38. Equations with an integral taken over a closed manifold 172
§ 39. Extension by means of the parameter 180
§ 40. Systems of singular integral equations 184
§ 41. Singular integral equations in classes of Lipschitz functions 190
VIII. MISCELLANEOUS APPLICATIONS 199
§ 42. Leading derivatives of volume potential 199
§ 43. Problem of the oblique derivative 203
§ 44. Inequality involving the tangential and normal components
of the gradient of a harmonic function 208
§ 45. Equilibrium of an isotropic elastic body 210
§ 46. Diffraction of stationary elastic waves 220
CONTENTS ix
APPENDIX. Multipliers of Fourier integrals 225
BIBLIOGRAPHY 241
INDEX 251
OTHER TITLES IN THE SERIES 257
|
| adam_txt |
CONTENTS
PREFACE xi
I. INTRODUCTION 1
§ 1. Review of previous work 1
§ 2. Some theorems on linear equations in Banaeh spaces 21
§ 3. Stereographic projection 30
§ 4. Completely continuous operators 32
H. SIMPLEST PROPERTIES OF MULTIDIMENSIONAL SINGULAR
INTEGRALS 37
§ 6. Basic concepts 37
§ 6. Lipschitz conditions 46
§ 7. Order of singular integrals at infinity 50
§ 8. Differentiation of integrals with a weak singularity 59
HI. COMPOUNDING OF SINGULAR INTEGRALS 63
§ 9. Compounding of singular and ordinary integrals 63
§ 10. Compounding of double singular integrals 67
§ 11. The concept of a singular operator 70
§ 12. Compounding of double singular integrals. The symbol 71
§ 13. Compounding of multidimensional singular integrals 72
§ 14. Formulae for reference 74
§ 15. Product of the operators A1 and An 77
§ 16. Product of the operators A% and An 81
§ 17. Calculation of nlm 83
§ 18. Symbol of a multidimensional singular integral 86
IV. PROPERTIES OF THE SYMBOL 93
§ 19. Fourier transform of a singular kernel 93
§ 20. Fourier transform of a kernel and the symbol of a singular
operator 97
§ 21. Transformation of the symbol under change of variables 104
vii
viii CONTENTS
§ 22. Differentiability of the symbol 109
§ 23. The conditions for the continuity of the symbol 112
V. SINGULAR INTEGRALS IN Lp SPACES 116
§ 24. The simplest corollaries from the Fourier transform. First
theorem on boundedness in L2 space 116
§ 25. Symbol dependent on the pole. Second theorem on bounded
ness in £2 space 119
§ 26. On the boundedness of a singular integral operator in Lp
space 123
§ 27. Integrals taken over any manifold 130
§ 28. Differential properties of singular integrals 131
VI. FURTHER INVESTIGATION OF THE SYMBOL 134
§ 29. More about the differentiation of integrals with a weak
singularity 134
§ 30. Polyharmonic potentials 135
§ 31. Series of spherical functions 136
§ 32. Differential properties of the symbol and the characteristic 148
§ 33. Rule for the multiplication of the symbols in the general case 150
§ 34. Conjugate singular operator 154
VII. SINGULAR INTEGRAL EQUATIONS 157
§ 35. The case where the symbol is independent of the pole 157
§ 36. The case where the symbol is dependent on pole. Regulariza
tion and domains of constancy of the index 158
§ 37. Equivalent regularization. Index theorem 160
§ 38. Equations with an integral taken over a closed manifold 172
§ 39. Extension by means of the parameter 180
§ 40. Systems of singular integral equations 184
§ 41. Singular integral equations in classes of Lipschitz functions 190
VIII. MISCELLANEOUS APPLICATIONS 199
§ 42. Leading derivatives of volume potential 199
§ 43. Problem of the oblique derivative 203
§ 44. Inequality involving the tangential and normal components
of the gradient of a harmonic function 208
§ 45. Equilibrium of an isotropic elastic body 210
§ 46. Diffraction of stationary elastic waves 220
CONTENTS ix
APPENDIX. Multipliers of Fourier integrals 225
BIBLIOGRAPHY 241
INDEX 251
OTHER TITLES IN THE SERIES 257 |
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| author | Michlin, Solomon G. 1908-1990 |
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| edition | 1. Engl. ed. |
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| id | DE-604.BV022011742 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T16:11:50Z |
| indexdate | 2024-07-09T20:49:13Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015226374 |
| oclc_num | 67441819 |
| open_access_boolean | |
| owner | DE-706 DE-188 |
| owner_facet | DE-706 DE-188 |
| physical | XII, 255 S. |
| publishDate | 1965 |
| publishDateSearch | 1965 |
| publishDateSort | 1965 |
| publisher | Pergamon Press |
| record_format | marc |
| series | International series of monographs in pure and applied mathematics |
| series2 | International series of monographs in pure and applied mathematics |
| spelling | Michlin, Solomon G. 1908-1990 Verfasser (DE-588)172258243 aut Mnogomernye singuljarnye integraly i integral'ny uravnenija Multidimensional singular integrals and integral equations by S. G. Mikhlin 1. Engl. ed. Oxford [u.a.] Pergamon Press 1965 XII, 255 S. txt rdacontent n rdamedia nc rdacarrier International series of monographs in pure and applied mathematics 83 Aus. dem Russ. übers. Singuläre Integralgleichung (DE-588)4181523-3 gnd rswk-swf Singuläres Integral (DE-588)4181533-6 gnd rswk-swf Integralgleichung (DE-588)4027229-1 gnd rswk-swf Integralgleichung (DE-588)4027229-1 s DE-604 Singuläres Integral (DE-588)4181533-6 s Singuläre Integralgleichung (DE-588)4181523-3 s 1\p DE-604 International series of monographs in pure and applied mathematics 83 (DE-604)BV001888024 83 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015226374&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Michlin, Solomon G. 1908-1990 Multidimensional singular integrals and integral equations International series of monographs in pure and applied mathematics Singuläre Integralgleichung (DE-588)4181523-3 gnd Singuläres Integral (DE-588)4181533-6 gnd Integralgleichung (DE-588)4027229-1 gnd |
| subject_GND | (DE-588)4181523-3 (DE-588)4181533-6 (DE-588)4027229-1 |
| title | Multidimensional singular integrals and integral equations |
| title_alt | Mnogomernye singuljarnye integraly i integral'ny uravnenija |
| title_auth | Multidimensional singular integrals and integral equations |
| title_exact_search | Multidimensional singular integrals and integral equations |
| title_exact_search_txtP | Multidimensional singular integrals and integral equations |
| title_full | Multidimensional singular integrals and integral equations by S. G. Mikhlin |
| title_fullStr | Multidimensional singular integrals and integral equations by S. G. Mikhlin |
| title_full_unstemmed | Multidimensional singular integrals and integral equations by S. G. Mikhlin |
| title_short | Multidimensional singular integrals and integral equations |
| title_sort | multidimensional singular integrals and integral equations |
| topic | Singuläre Integralgleichung (DE-588)4181523-3 gnd Singuläres Integral (DE-588)4181533-6 gnd Integralgleichung (DE-588)4027229-1 gnd |
| topic_facet | Singuläre Integralgleichung Singuläres Integral Integralgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015226374&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001888024 |
| work_keys_str_mv | AT michlinsolomong mnogomernyesinguljarnyeintegralyiintegralnyuravnenija AT michlinsolomong multidimensionalsingularintegralsandintegralequations |