p-Adic Multiresolution Analysis and Wavelet Frames

By Sergio Albeverio, Sergei Evdokimov, Maria Skopina. 2008

110 citations recorded by the source corpus.

We study p-adic multiresolution analyses (MRAs). A complete characterization of test functions generating an MRA (scaling functions) is given. We prove that only 1-periodic test functions may be taken as orthogonal scaling functions and that all such scaling functions generate the Haar MRA. We also suggest a method for constructing sets of wavelet functions and prove that any set of wavelet functions generates a p-adic wavelet frame.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f23fee431450150911f288005587641bfdfadf2e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. P. Auscher
2. Tuomas Hytönen
3. Branko Dragovich
4. Igor V. Volovich
5. Sergei V. Kozyrev
6. A. Khrennikov
7. Evgeny Zelenov
8. Q. Jahan

In Computational Theory and Mathematics

1. P. Auscher
2. Evgeny Zelenov
3. Sergei V. Kozyrev
4. Q. Jahan
5. A. Khrennikov
6. Branko Dragovich
7. Igor V. Volovich
8. Biswaranjan Behera

In Mathematical Physics

1. Q. Jahan
2. Biswaranjan Behera
3. Branko Dragovich
4. Igor V. Volovich
5. A. Khrennikov
6. Evgeny Zelenov
7. P. Auscher
8. Sergei V. Kozyrev

Citations in the corpus

• p-Adic mathematical physics: the first 30 years (2017, methodology): “Important contributions in p-adic wavelet theory were done also by Albeverio, Benedetto, Khrennikov, Shelkovich, Skopina, Evdokimov [41, 42, 6, 7, 143, 144, 222, 145, 15].”
• Orthonormal bases of regular wavelets in spaces of homogeneous type (2011, background): “To mention a few references in these directions, see [3], [35], [37].”
• Characterization of wavelets and MRA wavelets on local fields of positive characteristic (2013, background): “But later on in [2], Albeverio, Evdokimov and Skopina proved that all these scaling functions lead to the same Haar MRA and that there exist no other orthogonal test scaling functions generating an MRA except those described in [24].”