Oblique projections and abstract splines
Given a closed subspace L of a Hilbert space ℋ and a bounded linear operator A ∈ L(ℋ) which is positive, consider the set of all A-self-adjoint projections onto Y: ℘(A,Y) = {Q ∈ L(ℋ): Q2 = Q, Q(ℋ) = Y, AQ = Q*A}. In addition, if ℋ1 is another Hilbert space, T : ℋ → ℋ1 is a bounded linear operator su...
Guardado en:
| Autores principales: | , , |
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| Formato: | Articulo |
| Lenguaje: | Inglés |
| Publicado: |
2002
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| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/84951 |
| Aporte de: |
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I19-R120-10915-84951 |
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| record_format |
dspace |
| institution |
Universidad Nacional de La Plata |
| institution_str |
I-19 |
| repository_str |
R-120 |
| collection |
SEDICI (UNLP) |
| language |
Inglés |
| topic |
Matemática |
| spellingShingle |
Matemática Corach, Gustavo Maestripieri, A. Stojanoff, Demetrio Oblique projections and abstract splines |
| topic_facet |
Matemática |
| description |
Given a closed subspace L of a Hilbert space ℋ and a bounded linear operator A ∈ L(ℋ) which is positive, consider the set of all A-self-adjoint projections onto Y: ℘(A,Y) = {Q ∈ L(ℋ): Q2 = Q, Q(ℋ) = Y, AQ = Q*A}. In addition, if ℋ1 is another Hilbert space, T : ℋ → ℋ1 is a bounded linear operator such that T*T = A and ξ ∈ ℋ, consider the set of (T, Y) spline interpolants to ξ: sp(T, Y, ξ) = { η ε ξ + Y : ∥Tη∥ = min ∥T(ξ + σ)∥}. A strong relationship exists between ℘(A, Y) and s p(T, Y, ξ). In fact, ∥(A, Y) is not empty if and only if s p(T, Y, ξ) is not empty for every ξ ∈ ℋ. In this case, for any ξ ∈ ℋ\Y it holds s p(T, Y, ξ) = {(1 - Q)ξ:Q ∈ ℘(A, Y)} and for any ξ ∈ ℋ, the unique vector of s p(T, Y, ξ) with minimal norm is (1 - PA,Y)ξ, where PA,L is a distinguished element of ℘(A, Y). These results offer a generalization to arbitrary operators of several theorems by de Boor, Atteia, Sard and others, which hold for closed range operators. |
| format |
Articulo Articulo |
| author |
Corach, Gustavo Maestripieri, A. Stojanoff, Demetrio |
| author_facet |
Corach, Gustavo Maestripieri, A. Stojanoff, Demetrio |
| author_sort |
Corach, Gustavo |
| title |
Oblique projections and abstract splines |
| title_short |
Oblique projections and abstract splines |
| title_full |
Oblique projections and abstract splines |
| title_fullStr |
Oblique projections and abstract splines |
| title_full_unstemmed |
Oblique projections and abstract splines |
| title_sort |
oblique projections and abstract splines |
| publishDate |
2002 |
| url |
http://sedici.unlp.edu.ar/handle/10915/84951 |
| work_keys_str_mv |
AT corachgustavo obliqueprojectionsandabstractsplines AT maestripieria obliqueprojectionsandabstractsplines AT stojanoffdemetrio obliqueprojectionsandabstractsplines |
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Repositorios |
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1764820488759017472 |