Top

Published in:

2014 | OriginalPaper | Chapter

Interval Wavelet Sets Determined by Points on the Circle

Author : Divya Singh

Published in: Fractals, Wavelets, and their Applications

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

Having observed that an interval wavelet set corresponds to the points in a circle, we obtain points in the circle which characterize two-interval wavelet sets and also those points which characterize three-interval wavelet sets for dilation d ≥ 2. Further points in the circle characterizing one-interval and two-interval H ²-wavelet sets for dilation d ≥ 2 are obtained. In addition, we discuss three-interval wavelet sets of \(\mathbb{R}\) in respect of being associated with a multiresolution analysis (MRA).

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

previous chapter A New Class of Rational Quadratic Fractal Functions with Positive Shape Preservation

next chapter Inverse Representation Theorem for Matrix Polynomials and Multiscaling Functions

Arcozzi, N., Behera, B., Madan, S.: Large classes of minimally supported frequency wavelets of \(L^{2}\left (\mathbb{R}\right )\) and \(H^{2}\left (\mathbb{R}\right )\). J. Geom. Anal. 13, 557–579 (2003)MathSciNetCrossRefMATH

Baggett, L.W., Medina, H.A., Merrill, K.D.: Generalized multi-resolution analyses and a construction procedure for all wavelet sets in \(\mathbb{R}^{n}\). J. Fourier Anal. Appl. 5, 563–573 (1999)MathSciNetCrossRefMATH

Bownik, M., Hoover, K.: Dimension functions of rationally dilated GMRAs and wavelets. J. Fourier Anal. Appl. 15(5), 585–615 (2009)

Bownik, M., Rzeszotnik, Z., Speegle, D.: A characterization of dimension functions of wavelets. Appl. Comput. Harmon. Anal. 10, 71–92 (2001)MathSciNetCrossRefMATH

Dai, X., Larson, D.: Wandering vectors for unitary systems and orthogonal wavelets. Mem. Amer. Math. Soc. 134(640), MR 98m:47067. (1998)

Dai, X., Larson, D., Speegle, D.: Wavelet sets in \(\mathbb{R}^{n}\). J. Fourier Anal. Appl. 3, 451–456 (1997)MathSciNetCrossRefMATH

Dai, X., Larson, D., Speegle, D.: Wavelet sets in \(\mathbb{R}^{n}\) II. Contemp. Math. 216, 15–40 (1998)MathSciNetCrossRef

Singh, D.: On wavelet induced isomorphisms. Int. J. Wavelets Multiresolut. Inf. Process. 8(3), 359–371 (2010)MathSciNetCrossRefMATH

Fang, X., Wang, X.: Construction of minimally-supported-frequency wavelets. J. Fourier Anal. Appl. 2, 315–327 (1996)MathSciNetMATH

10.

Ha, Y., Kang, H., Lee, J., Seo, J.: Unimodular wavelets for L ² and the Hardy space H ². Michigan Math. J. 41, 345–361 (1994)MathSciNetCrossRefMATH

11.

Hernández, E., Weiss, G.: A First Course on Wavelets. CRC Press, Boca Raton (1996)CrossRefMATH

12.

Ionascu, E.: A new construction of wavelet sets. Real Anal. Exch. 28, 593–610 (2002/2003)

13.

Ionascu, E., Larson, D., Pearcy, C.: On wavelet sets. J. Fourier Anal. Appl. 4, 711–721 (1998)MathSciNetCrossRefMATH

14.

Merrill, K.D.: Simple wavelet sets for scalar dilations in \(\mathbb{R}^{2}\). In: Representations, Wavelets and Frames: A Celebration of the Mathematical Work of Lawrence W. Baggett, pp. 177–192. Birkhäuser, Boston (2008)

Title: Interval Wavelet Sets Determined by Points on the Circle
Author: Divya Singh
Publisher: Springer International Publishing
Book: Fractals, Wavelets, and their Applications
Print ISBN: 978-3-319-08104-5

Electronic ISBN: 978-3-319-08105-2

Copyright Year: 2014
DOI: https://doi.org/10.1007/978-3-319-08105-2_19

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Premium Partner