Hilbertian Kernels and spline functions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam u.a.
North-Holland
1992
|
| Series: | Studies in computational mathematics
4 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 386 S. |
| ISBN: | 0444897186 |
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MARC
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| 100 | 1 | |a Atteia, Marc |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Hilbertian Kernels and spline functions |c Marc Atteia |
| 264 | 1 | |a Amsterdam u.a. |b North-Holland |c 1992 | |
| 300 | |a XII, 386 S. | ||
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| 490 | 1 | |a Studies in computational mathematics |v 4 | |
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Record in the Search Index
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| adam_text | vii
CONTENTS
Chapter I s Hilbertian Kernels
1. Hilbertian subspaces of IR^ and associated Kernels 4
2. Bijection of the set of hilbertian subspaces of R0
onto IR?* 11
3. Support of a Kernel 18
4. Schwartz s Kernel of a hilbertian subspace of fif1
(resp. of a Locally convex space) 21
5 Ordered convex cone structure of Hilb (ff^Xresp. HILB (E)). .32
6. Image of an Hilbert subspace by a linear mapping and
its associated Kernel 40
7. Elementary operations onto Kernels of hilbertian sub¬
spaces 44
8. Tensor product of hilbertian subspaces and associated
Kernels 59
9. Quotient Hilbert subspaces. Associated semi Kernels 74
10. Kernels regularity 77
11. Hilbertian subspaces Kernels and quadratic convex
f unctionals 80
12. Complex Kernels. Bochner theorem 86
Chapter II : Interpolation. Approximation of linear func¬
tionals
A General formulation of the interpolation problem.
Dual problem. Sard s theorem
1. A general formulation of the interpolation problem 1 96
The dual problem I of the problem 1 97
2. Sard s factorization theorem 98
B Laorange and Newton interpolations
3. Lagrange interpolation 100
4. Basis change in the Lagrange interpolation 103
viii
5. Newton interpolation 106
6. Dual problem of the Lagrange interpolation. Error in
the Lagrange interpolation 110
7. Examples 112
C Interpolation with an infinity of data
8. Some preliminary results about the bases of topolo
gical vector spaces 121
9. Interpolation with an infinity of data 130
10. Frames 136
Chapter III : Interpolating and smoothing spline
(or Schoenberg) functions
1. Interpolating spline functions (i.s.f.) 146
2. Smoothing spline functions (s.s.f.) ...152
3. Spline functions and (semi ) hilbertian Kernels 156
4. Examples of spline functions (or Schoenberg functions) 164
Chapter IV : Operations on spline functions
1. Image spline function 175
2. Direct Hilbert sum and cartesian product of spline func¬
tions 178
3. Sum of spline functions 182
4. Tensor product of spline functions 183
5. Relations between the operations on spline functions
and operations on hilbertian Kernels 190
Chapter V t Internal and external convergence of spline
functions
ft Interpolating functions
1. About internal and external convergences 197
2. Internal convergence of the i.s.f 199
3. External convergence of the i.s.f 212
4. Convergence of a tensor product of i.s.f 216
ix
B Smoothing spline functions
5. Internal convergence of the smoothing spline
functions 222
Chapter VI Spline functions onto a convex set
A The primal problem
1. Interpolating spline function on a convex set.
Primal problem. First properties 232
2. Conditions of closure of u(G) 234
3. Study of the set f^. 241
B The dual problem
4. Equivalence of the problem 3* and a convex optimi¬
zation problem without constraint 250
5. Duality 253
6. Smooth spline function on a convex set 268
Chapter VII Spline manifolds and linear elasticity
1. Elementary notions of tridimensional elasticity 281
2. Linear elasticity and spline functions 283
3. Spline manifold on an open set Q 288
4. Spline manifold relating to a partial differential
operator 297
Chapter VIII B splines, Box splines, Simplicial splines
A B splines
1. The Hilbert space Lm 328
2. B spline 329
X
B Box splines
3. Box splines Basic properties 342
4. Examples of Box splines .345
5 .The Box splines revisited 349
C Simplicial splines
6. Generalized barycentric coordinates 357
7. Hilbertian representation of a simplicial complex 358
8. A basic application 361
9. Elementary operations on hilbertian representations of
simplicial complexes 363
COMMENTS 369
BIBLIOGRAPHY 373
|
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| id | DE-604.BV007995788 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:12:47Z |
| institution | BVB |
| isbn | 0444897186 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005265499 |
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| physical | XII, 386 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | North-Holland |
| record_format | marc |
| series | Studies in computational mathematics |
| series2 | Studies in computational mathematics |
| spelling | Atteia, Marc Verfasser aut Hilbertian Kernels and spline functions Marc Atteia Amsterdam u.a. North-Holland 1992 XII, 386 S. txt rdacontent n rdamedia nc rdacarrier Studies in computational mathematics 4 Noyaux (Mathématiques) ram Splines, théorie des ram Kernel functions Spline theory Spline-Funktion (DE-588)4056332-7 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Spline-Funktion (DE-588)4056332-7 s Hilbert-Raum (DE-588)4159850-7 s DE-604 Studies in computational mathematics 4 (DE-604)BV001895633 4 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005265499&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Atteia, Marc Hilbertian Kernels and spline functions Studies in computational mathematics Noyaux (Mathématiques) ram Splines, théorie des ram Kernel functions Spline theory Spline-Funktion (DE-588)4056332-7 gnd Hilbert-Raum (DE-588)4159850-7 gnd |
| subject_GND | (DE-588)4056332-7 (DE-588)4159850-7 |
| title | Hilbertian Kernels and spline functions |
| title_auth | Hilbertian Kernels and spline functions |
| title_exact_search | Hilbertian Kernels and spline functions |
| title_full | Hilbertian Kernels and spline functions Marc Atteia |
| title_fullStr | Hilbertian Kernels and spline functions Marc Atteia |
| title_full_unstemmed | Hilbertian Kernels and spline functions Marc Atteia |
| title_short | Hilbertian Kernels and spline functions |
| title_sort | hilbertian kernels and spline functions |
| topic | Noyaux (Mathématiques) ram Splines, théorie des ram Kernel functions Spline theory Spline-Funktion (DE-588)4056332-7 gnd Hilbert-Raum (DE-588)4159850-7 gnd |
| topic_facet | Noyaux (Mathématiques) Splines, théorie des Kernel functions Spline theory Spline-Funktion Hilbert-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005265499&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001895633 |
| work_keys_str_mv | AT atteiamarc hilbertiankernelsandsplinefunctions |