Cubature formulas and modern analysis: an introduction
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Philadelphia, Pa. [u.a.]
Gordon and Breach Science Publ.
1992
|
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005876282&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | XVI, 379 S. Ill., graph. Darst. |
| ISBN: | 2881248411 |
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MARC
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| 240 | 1 | 0 | |a Vvedenie v teoriju kubaturnich formul |
| 245 | 1 | 0 | |a Cubature formulas and modern analysis |b an introduction |c S. L. Sobolev |
| 264 | 1 | |a Philadelphia, Pa. [u.a.] |b Gordon and Breach Science Publ. |c 1992 | |
| 300 | |a XVI, 379 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Aus dem Russ. übers. | ||
| 650 | 4 | |a Cubature formulas | |
| 650 | 4 | |a Mathematical analysis | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
PREFACE TO THE ENGLISH EDITION ix
PREFACE TO THE RUSSIAN EDITION xiii
CHAPTER I. BASIC CONCEPTS AND FORMULATIONS 1
§ 1. Concepts in Linear Algebra 1
§ 2. Point Lattices 6
§ 3. Some Functional Spaces 11
§ 4. Generalized Derivatives and Primitive Functions 22
§ 5. Density of Finite Functions 32
§ 6. Principal Embedding Theorems for Weighted Spaces 36
§ 7. Functions of a Discrete Argument 46
§ 8. Generalized Functions 54
§ 9. Fourier Transformation of Generalized Functions 69
§10. Periodic Functions and Generalized Functions 77
§11. Generalized Spherical Harmonics 86
CHAPTER II. POLYHARMONIC EQUATION 96
§ 1. Green s Formula 96
§ 2. Fundamental Solution of a Polyharmonic Equation 102
§ 3. Differential Properties of Solutions of a Polyharmonic
Equation 106
§ 4. Behavior of Polyharmonic Functions in the Neighborhood
of Infinity 111
vi
§ 5. Almansi s Theorem and Kelvin Transformation 113
§ 6. Principal Solutions of a Polyharmonic Equation 121
§ 7. Expansion of Polyharmonic Functions in Principal
Solutions 135
§ 8. Polyharmonic Functions from W2 in the Neighborhood
of Infinity 145
§ 9. Boundary Value Problems for a Polyharmonic Equation in
a Bounded Domain 147
§10. Kelvin Problem in an Infinite Domain 160
§11. Exterior Variational Problem for a Polyharmonic Equation 167
§12. Extension of a Function from the Region fi on Rn with the
Least Norm 177
§13. Values of Functions from W^m) at the Lattice Points 184
§14. Explicit Method of Regularization of Divergent Integrals 189
CHAPTER HI. TWO SIMPLE PROBLEMS OF THE
THEORY OF COMPUTATIONS 200
§ 1. Interpolation 200
§ 2. Construction of Cubature Formulas 205
§ 3. Functional Formulation of the Problems. Extremal Function
of a Cubature Formula 208
§ 4. Error Functional in W$m)(Rn) 215
§ 5. Square of the Norm of the Error Functional 218
§ 6. Deviation of Error of a Cubature Formula from the
Optimal 222
§ 7. Appendix 224
CHAPTER IV. ORDER OF CONVERGENCE OF
CUBATURE FORMULAS 230
§ 1. Lower Estimate of the Norm of the Error Functional 230
§ 2. Approximate Upper Estimate of the Norm of the Error
Functional 236
vii
CHAPTER V. CUBATURE FORMULAS CONSIDERING A
REGULAR BOUNDARY LAYER 247
§ 1. Formulas for Periodic Functions 247
§ 2. Norm of the Error Functional for Periodic Functions 251
§ 3. Composition of Formulas with Small Supports 254
§ 4. Error for Finite Functions 258
§ 5. Construction of Formulas with a Regular Boundary Layer 270
§ 6. Norm of the Error Functional of Cubature Formulas with a
Regular Boundary Layer in the Space L{2my(Rn) 276
§ 7. Norm of the Error of Formulas with Regular Boundary
Layer in 4m)(n) 287
CHAPTER VI. OPTIMAL FORMULAS 290
§ 1. Formulation of the Problem on Optimal Coefficients 290
§ 2. Fourier Transformation of a Discrete Potential 296
§ 3. Properties of the Operator!) ^[3]* 300
§ 4. Discrete Analog of a Polyharmonic Operator 306
§ 5. Optimal Coefficients of One Dimensional Formulas 319
CHAPTER VII. CONVERGENCE OF CUBATURE
FORMULAS IN VARIOUS CLASSES AND
DIFFERENT FUNCTIONS 325
§ 1. Functional Class $((3|A) 325
§ 2. Functional Class *(p|a) 333
§ 3. Cubature Formulas for Infinitely Differentiable Functions 340
§ 4. Convergence of Cubature Formulas for an Arbitrary
Function ip(a;) € L(2m) 344
CHAPTER VIII. CUBATURE FORMULAS FOR RATIONAL
POLYHEDRA 347
§ 1. Convex Polyhedra. Euler s Formula 347
§ 2. Rational Polyhedra 355
viii
§ 3. Structure of Formulas for Rational Polyhedra 358
§ 4. Cubature Formulas for a Polyhedron and Its Solid Angles 360
§ 5. Formulas with a Formal Boundary Layer 362
BIBLIOGRAPHY 369
INDEX 377
|
| any_adam_object | 1 |
| author | Sobolev, S. L. 1908-1989 |
| author_GND | (DE-588)119002833 |
| author_facet | Sobolev, S. L. 1908-1989 |
| author_role | aut |
| author_sort | Sobolev, S. L. 1908-1989 |
| author_variant | s l s sl sls |
| building | Verbundindex |
| bvnumber | BV008883131 |
| callnumber-first | Q - Science |
| callnumber-label | QA299 |
| callnumber-raw | QA299.4.C83 |
| callnumber-search | QA299.4.C83 |
| callnumber-sort | QA 3299.4 C83 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 400 SK 780 |
| ctrlnum | (OCoLC)24847525 (DE-599)BVBBV008883131 |
| dewey-full | 515/.624 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.624 |
| dewey-search | 515/.624 |
| dewey-sort | 3515 3624 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV008883131 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T09:28:41Z |
| institution | BVB |
| isbn | 2881248411 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005876282 |
| oclc_num | 24847525 |
| open_access_boolean | |
| owner | DE-703 DE-355 DE-BY-UBR DE-824 DE-29T DE-83 |
| owner_facet | DE-703 DE-355 DE-BY-UBR DE-824 DE-29T DE-83 |
| physical | XVI, 379 S. Ill., graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Gordon and Breach Science Publ. |
| record_format | marc |
| spellingShingle | Sobolev, S. L. 1908-1989 Cubature formulas and modern analysis an introduction Cubature formulas Mathematical analysis Kubaturformel (DE-588)4294387-5 gnd |
| subject_GND | (DE-588)4294387-5 |
| title | Cubature formulas and modern analysis an introduction |
| title_alt | Vvedenie v teoriju kubaturnich formul |
| title_auth | Cubature formulas and modern analysis an introduction |
| title_exact_search | Cubature formulas and modern analysis an introduction |
| title_full | Cubature formulas and modern analysis an introduction S. L. Sobolev |
| title_fullStr | Cubature formulas and modern analysis an introduction S. L. Sobolev |
| title_full_unstemmed | Cubature formulas and modern analysis an introduction S. L. Sobolev |
| title_short | Cubature formulas and modern analysis |
| title_sort | cubature formulas and modern analysis an introduction |
| title_sub | an introduction |
| topic | Cubature formulas Mathematical analysis Kubaturformel (DE-588)4294387-5 gnd |
| topic_facet | Cubature formulas Mathematical analysis Kubaturformel |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005876282&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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