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010   $a3-319-99175-2
024 7 $a10.1007/978-3-319-99175-7
035   $a(CKB)4100000007003160
035   $a(MiAaPQ)EBC5553266
035   $a(DE-He213)978-3-319-99175-7
035   $a(PPN)231461623
035   $a(EXLCZ)994100000007003160
100   $a20181011d2018      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aGeneralized Multiresolution Analyses /$fby Kathy D. Merrill
205   $a1st ed. 2018.
210  1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2018.
215   $a1 online resource (121 pages)
225 1 $aLecture Notes in Applied and Numerical Harmonic Analysis,$x2512-6482
311   $a3-319-99174-4 
327   $aIntroduction -- The Invariance of the Core Subspace -- The Multiplicity Function -- Wavelet Sets -- Generalized Filters -- Fractal Spaces -- Composite Dilations and Crystallographic Groups -- Abstract Constructions of GMRAs.
330   $aThis monograph presents the first unified exposition of generalized multiresolution analyses. Expanding on the author?s pioneering work in the field, these lecture notes provide the tools and framework for using GMRAs to extend results from classical wavelet analysis to a more general setting. Beginning with the basic properties of GMRAs, the book goes on to explore the multiplicity and dimension functions of GMRA, wavelet sets, and generalized filters. The author?s constructions of wavelet sets feature prominently, with figures to illustrate their remarkably simple geometric form. The last three chapters exhibit extensions of wavelet theory and GMRAs to other settings. These include fractal spaces, wavelets with composite dilations, and abstract constructions of GMRAs beyond the usual setting of L2(?n). This account of recent developments in wavelet theory will appeal to researchers and graduate students with an interest in multiscale analysis from a pure or applied perspective. Familiarity with harmonic analysis and operator theory will be helpful to the reader, though the only prerequisite is graduate level experience with real and functional analysis.
410  0$aLecture Notes in Applied and Numerical Harmonic Analysis,$x2512-6482
606   $aHarmonic analysis
606   $aFunctional analysis
606   $aMeasure theory
606   $aAbstract Harmonic Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12015
606   $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066
606   $aMeasure and Integration$3https://scigraph.springernature.com/ontologies/product-market-codes/M12120
615  0$aHarmonic analysis.
615  0$aFunctional analysis.
615  0$aMeasure theory.
615 14$aAbstract Harmonic Analysis.
615 24$aFunctional Analysis.
615 24$aMeasure and Integration.
676   $a515
700   $aMerrill$b Kathy D$4aut$4http://id.loc.gov/vocabulary/relators/aut$0768256
906   $aBOOK
912   $a9910300129803321
996   $aGeneralized Multiresolution Analyses$91564746
997   $aUNINA