RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB General information Latest issue Archive Impact factor Subscription Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Sib. Zh. Vychisl. Mat.: Year: Volume: Issue: Page: Find

 Personal entry: Login: Password: Save password Enter Forgotten password? Register

 Sib. Zh. Vychisl. Mat., 2004, Volume 7, Number 3, Pages 261–275 (Mi sjvm162) Multiresolution analysis in the space $\ell^2(\mathbb Z)$ using discrete splines

A. B. Pevnyi

Syktyvkar State University, Faculty of Mathematics

Abstract: A non-stationary multiresolution analysis $\{V_k\}_{k\geq 0}$ $\ell^2(\mathbb Z)$ in the space $\ell^2(\mathbb Z)$ is performed, the subspaces $V_k$ consisting of discrete splines. In each $V_k$, there is a function $\varphi_k$ such that the system $\{\varphi_k(\cdot-l2^k):l\in\mathbb Z\}$ forms the Riesz base of $V_k$. A system of wavelets $\psi_{kl}(j)=\psi_k(j-l2^k)$, $l\in\mathbb Z$, $k=1,2…$ is not generated by shifts and dilations of the unique function. The subspaces $W_k=\operatorname{span}\{\psi_{kl}:l\in\mathbb Z\}$ form an orthogonal expansion of the space: $\ell^2(\mathbb Z)=\oplus^{\infty}_{k=1}W_k$.
The space $V_k$ is the same as the space of discrete splines $S_{p,2^k}$ of order $p$ with a distance between the knots $2^k$. For every $p$, a multiresolution analysis is obtained (for $p=1$ – the Haar multiresolution analysis).

Key words: discrete splines, discrete wavelets, multiresolution analysis. Full text: PDF file (759 kB) References: PDF file   HTML file

Bibliographic databases: UDC: 519.65

Citation: A. B. Pevnyi, “Multiresolution analysis in the space $\ell^2(\mathbb Z)$ using discrete splines”, Sib. Zh. Vychisl. Mat., 7:3 (2004), 261–275 Citation in format AMSBIB
\Bibitem{Pev04} \by A.~B.~Pevnyi \paper Multiresolution analysis in the space $\ell^2(\mathbb Z)$ using discrete splines \jour Sib. Zh. Vychisl. Mat. \yr 2004 \vol 7 \issue 3 \pages 261--275 \mathnet{http://mi.mathnet.ru/sjvm162} \zmath{https://zbmath.org/?q=an:1068.65152} 

 SHARE: • Contact us: math-net2019_11 [at] mi-ras ru Terms of Use Registration Logotypes © Steklov Mathematical Institute RAS, 2019
{"ft_lang_label":"__label__en","ft_lang_prob":0.59591836,"math_prob":0.9871759,"size":1957,"snap":"2019-43-2019-47","text_gpt3_token_len":656,"char_repetition_ratio":0.14029698,"word_repetition_ratio":0.0781893,"special_character_ratio":0.31323454,"punctuation_ratio":0.1825,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9989821,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68],"im_url_duplicate_count":[null,10,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-11-12T10:26:04Z\",\"WARC-Record-ID\":\"<urn:uuid:f9402639-5c59-4788-993a-26b4aadaab7d>\",\"Content-Length\":\"25519\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:aadb8c2b-c21c-4a8d-9449-b6be4e654065>\",\"WARC-Concurrent-To\":\"<urn:uuid:275c31af-5cc0-49e3-9a86-e35bfc5c5cf7>\",\"WARC-IP-Address\":\"185.129.147.141\",\"WARC-Target-URI\":\"http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=sjvm&paperid=162&option_lang=eng\",\"WARC-Payload-Digest\":\"sha1:S2XVNSLPHHA6KA47G6AJDECJUY7SRORU\",\"WARC-Block-Digest\":\"sha1:PALBKYSLPTCIAAFTRCV4D2AHPPOPPK5O\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-47/CC-MAIN-2019-47_segments_1573496665521.72_warc_CC-MAIN-20191112101343-20191112125343-00259.warc.gz\"}"}