{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:28:21Z","timestamp":1772296101824,"version":"3.50.1"},"reference-count":10,"publisher":"American Mathematical Society (AMS)","issue":"221","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>The theory of fiberization is applied to yield compactly supported tight affine frames (wavelets) in <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L 2 left-parenthesis double-struck upper R Superscript d Baseline right-parenthesis\">\n  <mml:semantics>\n    <mml:mrow>\n      <mml:msub>\n        <mml:mi>L<\/mml:mi>\n        <mml:mrow class=\"MJX-TeXAtom-ORD\">\n          <mml:mn>2<\/mml:mn>\n        <\/mml:mrow>\n      <\/mml:msub>\n      <mml:mo stretchy=\"false\">(<\/mml:mo>\n      <mml:msup>\n        <mml:mrow class=\"MJX-TeXAtom-ORD\">\n          <mml:mi mathvariant=\"double-struck\">R<\/mml:mi>\n        <\/mml:mrow>\n        <mml:mrow class=\"MJX-TeXAtom-ORD\">\n          <mml:mi>d<\/mml:mi>\n        <\/mml:mrow>\n      <\/mml:msup>\n      <mml:mo stretchy=\"false\">)<\/mml:mo>\n    <\/mml:mrow>\n    <mml:annotation encoding=\"application\/x-tex\">L_{2}(\\mathbb {R}^{d})<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula> from box splines. The wavelets obtained are smooth piecewise-polynomials on a simple mesh; furthermore, they exhibit a wealth of symmetries, and have a relatively small support. The number of \u201cmother wavelets\u201d, however, increases with the increase of the required smoothness. Two bivariate constructions, of potential practical value, are highlighted. In both, the wavelets are derived from four-direction mesh box splines that are refinable with respect to the dilation matrix <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"Start 1 By 3 Matrix 1st Row 1st Column 1 2nd Column a m p semicolon 1 1 3rd Column a m p semicolon negative 1 EndMatrix\">\n  <mml:semantics>\n    <mml:mrow>\n      <mml:mo>(<\/mml:mo>\n      <mml:mtable rowspacing=\"4pt\" columnspacing=\"1em\">\n        <mml:mtr>\n          <mml:mtd>\n            <mml:mn>1<\/mml:mn>\n          <\/mml:mtd>\n          <mml:mtd>\n            <mml:mi>a<\/mml:mi>\n            <mml:mi>m<\/mml:mi>\n            <mml:mi>p<\/mml:mi>\n            <mml:mo>;<\/mml:mo>\n            <mml:mn>1<\/mml:mn>\n            <mml:mtext>\u00a0<\/mml:mtext>\n            <mml:mn>1<\/mml:mn>\n          <\/mml:mtd>\n          <mml:mtd>\n            <mml:mi>a<\/mml:mi>\n            <mml:mi>m<\/mml:mi>\n            <mml:mi>p<\/mml:mi>\n            <mml:mo>;<\/mml:mo>\n            <mml:mo>\u2212<\/mml:mo>\n            <mml:mn>1<\/mml:mn>\n          <\/mml:mtd>\n        <\/mml:mtr>\n      <\/mml:mtable>\n      <mml:mo>)<\/mml:mo>\n    <\/mml:mrow>\n    <mml:annotation encoding=\"application\/x-tex\">\\begin {pmatrix}1&amp;1\\ 1&amp;-1\\end {pmatrix}<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula>.<\/p>","DOI":"10.1090\/s0025-5718-98-00898-9","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T22:14:44Z","timestamp":1027721684000},"page":"191-207","source":"Crossref","is-referenced-by-count":65,"title":["Compactly supported tight affine spline frames in \ud835\udc3f\u2082(\u211d^{\ud835\udd55})"],"prefix":"10.1090","volume":"67","author":[{"given":"Amos","family":"Ron","sequence":"first","affiliation":[]},{"given":"Zuowei","family":"Shen","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1998]]},"reference":[{"key":"1","series-title":"Applied Mathematical Sciences","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2244-4","volume-title":"Box splines","volume":"98","author":"de Boor, C.","year":"1993","ISBN":"https:\/\/id.crossref.org\/isbn\/0387941010"},{"issue":"1","key":"2","doi-asserted-by":"publisher","first-page":"51","DOI":"10.4171\/RMI\/133","article-title":"Nonseparable bidimensional wavelet bases","volume":"9","author":"Cohen, Albert","year":"1993","journal-title":"Rev. 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