國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Generalized multiresolution analyses

Merrill, Kathy D.

Generalized multiresolution analyses

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Generalized multiresolution analysesby Kathy D. Merrill.
作者:	Merrill, Kathy D.
出版者:	Cham :Springer International Publishing :2018.
面頁冊數:	x, 113 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Mathematical analysis.
電子資源:	https://doi.org/10.1007/978-3-319-99175-7
ISBN:	9783319991757$q(electronic bk.)

Generalized multiresolution analyses
Merrill, Kathy D.

Generalized multiresolution analyses[electronic resource] /by Kathy D. Merrill. - Cham :Springer International Publishing :2018. - x, 113 p. :ill., digital ;24 cm. - Lecture notes in applied and numerical harmonic analysis,2512-6482. - Lecture notes in applied and numerical harmonic analysis..

Introduction -- The Invariance of the Core Subspace -- The Multiplicity Function -- Wavelet Sets -- Generalized Filters -- Fractal Spaces -- Composite Dilations and Crystallographic Groups -- Abstract Constructions of GMRAs.

This 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(ℝn) 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.

ISBN: 9783319991757$q(electronic bk.)

Standard No.: 10.1007/978-3-319-99175-7doiSubjects--Topical Terms:

186133
Mathematical analysis.

LC Class. No.: QA300 / .M477 2018

Dewey Class. No.: 515

Generalized multiresolution analyses
LDR:02432nmm a2200337 a 4500 001 545801
003 DE-He213
005 20190326133224.0
006 m d
007 cr nn 008maaau
008 190530s2018 gw s 0 eng d
020 $a 9783319991757$q(electronic bk.)
020 $a 9783319991740$q(paper)
024 7 $a 10.1007/978-3-319-99175-7 $2 doi
035 $a 978-3-319-99175-7
040 $a GP $c GP
041 0 $a eng
050 4 $a QA300 $b .M477 2018
072 7 $a PBKD $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKD $2 thema
082 0 4 $a 515 $2 23
090 $a QA300 $b .M571 2018
100 1 $a Merrill, Kathy D. $3 591821
245 1 0 $a Generalized multiresolution analyses $h [electronic resource] / $c by Kathy D. Merrill.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2018.
300 $a x, 113 p. : $b ill., digital ; $c 24 cm.
490 1 $a Lecture notes in applied and numerical harmonic analysis, $x 2512-6482
505 0 $a Introduction -- The Invariance of the Core Subspace -- The Multiplicity Function -- Wavelet Sets -- Generalized Filters -- Fractal Spaces -- Composite Dilations and Crystallographic Groups -- Abstract Constructions of GMRAs.
520 $a This 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(ℝn) 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.
650 0 $a Mathematical analysis. $3 186133
650 1 4 $a Abstract Harmonic Analysis. $3 274074
650 2 4 $a Functional Analysis. $3 274845
650 2 4 $a Measure and Integration. $3 273777
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Lecture notes in applied and numerical harmonic analysis. $3 824883
856 4 0 $u https://doi.org/10.1007/978-3-319-99175-7
950 $a Mathematics and Statistics (Springer-11649)