Matches in SemOpenAlex for { <https://semopenalex.org/work/W2950647079> ?p ?o ?g. }
Showing items 1 to 83 of
83
with 100 items per page.
- W2950647079 abstract "In this paper we offer a computational approach to the spectral function for a finite family of commuting operators, and give applications. Motivated by questions in wavelets and in signal processing, we study a problem about spectral concentration of integral translations of functions in the Hilbert space $L^{2}(mathbb{R}^{n})$. Our approach applies more generally to families of $n$ arbitrary commuting unitary operators in a complex Hilbert space $mathcal{H}$, or equivalent the spectral theory of a unitary representation $U$ of the rank-$n$ lattice $mathbb{Z}^{n}$ in $mathbb{R}^{n}$. Starting with a non-zero vector $psi in mathcal{H}$, we look for relations among the vectors in the cyclic subspace in $mathcal{H}$ generated by $psi$. Since these vectors ${U(k)psi | k in mathbb{Z}^{n}}$ involve infinite ``linear combinations, the problem arises of giving geometric characterizations of these non-trivial linear relations. A special case of the problem arose initially in work of Kolmogorov under the name $L^{2}$-independence. This refers to textit{infinite} linear combinations of integral translates of a fixed function with $l^{2}$-coefficients. While we were motivated by the study of translation operators arising in wavelet and frame theory, we stress that our present results are general; our theorems are about spectral densities for general unitary operators, and for stochastic integrals." @default.
- W2950647079 created "2019-06-27" @default.
- W2950647079 creator A5021438721 @default.
- W2950647079 creator A5058575589 @default.
- W2950647079 date "2007-11-30" @default.
- W2950647079 modified "2023-09-27" @default.
- W2950647079 title "Optimal Decompositions of Translations of $L^{2}$-functions" @default.
- W2950647079 cites W1500590136 @default.
- W2950647079 cites W1555554612 @default.
- W2950647079 cites W1606802555 @default.
- W2950647079 cites W1797879437 @default.
- W2950647079 cites W1970787953 @default.
- W2950647079 cites W1976462044 @default.
- W2950647079 cites W1977271534 @default.
- W2950647079 cites W2003176204 @default.
- W2950647079 cites W2153647670 @default.
- W2950647079 cites W2157215689 @default.
- W2950647079 cites W2947000318 @default.
- W2950647079 cites W301883692 @default.
- W2950647079 hasPublicationYear "2007" @default.
- W2950647079 type Work @default.
- W2950647079 sameAs 2950647079 @default.
- W2950647079 citedByCount "0" @default.
- W2950647079 crossrefType "posted-content" @default.
- W2950647079 hasAuthorship W2950647079A5021438721 @default.
- W2950647079 hasAuthorship W2950647079A5058575589 @default.
- W2950647079 hasConcept C114614502 @default.
- W2950647079 hasConcept C118615104 @default.
- W2950647079 hasConcept C13336665 @default.
- W2950647079 hasConcept C134306372 @default.
- W2950647079 hasConcept C142730499 @default.
- W2950647079 hasConcept C17744445 @default.
- W2950647079 hasConcept C199539241 @default.
- W2950647079 hasConcept C202444582 @default.
- W2950647079 hasConcept C3019018024 @default.
- W2950647079 hasConcept C33923547 @default.
- W2950647079 hasConcept C34388435 @default.
- W2950647079 hasConcept C43929395 @default.
- W2950647079 hasConcept C62799726 @default.
- W2950647079 hasConcept C67820243 @default.
- W2950647079 hasConcept C98306654 @default.
- W2950647079 hasConceptScore W2950647079C114614502 @default.
- W2950647079 hasConceptScore W2950647079C118615104 @default.
- W2950647079 hasConceptScore W2950647079C13336665 @default.
- W2950647079 hasConceptScore W2950647079C134306372 @default.
- W2950647079 hasConceptScore W2950647079C142730499 @default.
- W2950647079 hasConceptScore W2950647079C17744445 @default.
- W2950647079 hasConceptScore W2950647079C199539241 @default.
- W2950647079 hasConceptScore W2950647079C202444582 @default.
- W2950647079 hasConceptScore W2950647079C3019018024 @default.
- W2950647079 hasConceptScore W2950647079C33923547 @default.
- W2950647079 hasConceptScore W2950647079C34388435 @default.
- W2950647079 hasConceptScore W2950647079C43929395 @default.
- W2950647079 hasConceptScore W2950647079C62799726 @default.
- W2950647079 hasConceptScore W2950647079C67820243 @default.
- W2950647079 hasConceptScore W2950647079C98306654 @default.
- W2950647079 hasLocation W29506470791 @default.
- W2950647079 hasOpenAccess W2950647079 @default.
- W2950647079 hasPrimaryLocation W29506470791 @default.
- W2950647079 hasRelatedWork W1490865937 @default.
- W2950647079 hasRelatedWork W1495567492 @default.
- W2950647079 hasRelatedWork W2006512386 @default.
- W2950647079 hasRelatedWork W2021269234 @default.
- W2950647079 hasRelatedWork W2029148579 @default.
- W2950647079 hasRelatedWork W2031216497 @default.
- W2950647079 hasRelatedWork W2049837379 @default.
- W2950647079 hasRelatedWork W2077919233 @default.
- W2950647079 hasRelatedWork W2184328006 @default.
- W2950647079 hasRelatedWork W2243470943 @default.
- W2950647079 hasRelatedWork W2282023504 @default.
- W2950647079 hasRelatedWork W2766512868 @default.
- W2950647079 hasRelatedWork W2951345776 @default.
- W2950647079 hasRelatedWork W2952668473 @default.
- W2950647079 hasRelatedWork W2953335114 @default.
- W2950647079 hasRelatedWork W2960215764 @default.
- W2950647079 hasRelatedWork W2963325462 @default.
- W2950647079 hasRelatedWork W2997874892 @default.
- W2950647079 hasRelatedWork W3094019438 @default.
- W2950647079 hasRelatedWork W3102685163 @default.
- W2950647079 isParatext "false" @default.
- W2950647079 isRetracted "false" @default.
- W2950647079 magId "2950647079" @default.
- W2950647079 workType "article" @default.