p-Adic wavelets and their applications

Козырев, С. В.; Khrennikov, Andrei; Shelkovich, V. M.

doi:10.1134/s0081543814040129

Cited by 14 publications

(11 citation statements)

References 76 publications

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“…There are many books and reviews which are useful for mathematical background of p-adic mathematical physics, see e.g. [308,137,53,99,18,1,171,172,170,163,199,304,120].…”

Section: Mathematical Backgroundmentioning

confidence: 99%

“…p-Adic wavelet theory was initiated by Kozyrev [175]. For the review of p-adic wavelets see [172]. 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].…”

Section: P-adic Waveletsmentioning

confidence: 99%

“…This modeling heavily explores theory of p-adic pseudodifferential equations, equations with fractional differential operators D α (Vladimirov's operators), see, e.g. [163,175,176,1,143,172,140,173,174]. In particular, to find solutions of p-adic master equations of the diffusion type one uses theory of p-adic wavelets established by S. Kozyrev [175,176], see [1,143,172] for its further development.…”

Section: Application Of P-adic Analysis To Geologymentioning

confidence: 99%

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p-Adic mathematical physics: the first 30 years

Драгович

Khrennikov

Козырев

et al. 2017

P-Adic Num Ultrametr Anal Appl

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130

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p-Adic mathematical physics is a branch of modern mathematical physics based on the application of p-adic mathematical methods in modeling physical and related phenomena. It emerged in 1987 as a result of efforts to find a non-Archimedean approach to the spacetime and string dynamics at the Planck scale, but then was extended to many other areas including biology. This paper contains a brief review of main achievements in some selected topics of p-adic mathematical physics and its applications, especially in the last decade. Attention is mainly paid to developments with promising future prospects.

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“…There are many books and reviews which are useful for mathematical background of p-adic mathematical physics, see e.g. [308,137,53,99,18,1,171,172,170,163,199,304,120].…”

Section: Mathematical Backgroundmentioning

confidence: 99%

Section: P-adic Waveletsmentioning

confidence: 99%

Section: Application Of P-adic Analysis To Geologymentioning

confidence: 99%

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p-Adic mathematical physics: the first 30 years

Драгович

Khrennikov

Козырев

et al. 2017

P-Adic Num Ultrametr Anal Appl

Self Cite

130

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show abstract

“…To resolve the obtained system (13)-(15) we use the basis of wavelets, constructed by analogy with the basis of p-adic wavelets [34,35]. To build the basis vectors we utilize the The total number of vectors is p , their orthogonality follows from orthogonality of vectors e k and the mutual orthogonality of χ j and q.…”

Section: Taking the Operation Of Intersection Inmentioning

confidence: 99%

Wavelet Analysis on Symbolic Sequences and Two-Fold de Bruijn Sequences

Osipov

2016

J Stat Phys

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Abstract. The concept of symbolic sequences play important role in study of complex systems. In the work we are interested in ultrametric structure of the set of cyclic sequences naturally arising in theory of dynamical systems. Aimed at construction of analytic and numerical methods for investigation of clusters we introduce operator language on the space of symbolic sequences and propose an approach based on wavelet analysis for study of the cluster hierarchy. The analytic power of the approach is demonstrated by derivation of a formula for counting of two-fold de Bruijn sequences, the extension of the notion of de Bruijn sequences. Possible advantages of the developed description is also discussed in context of applied problem of construction of efficient DNA sequence assembly algorithms.

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“…Moreover, these systems form Riesz bases without any dual wavelet systems. For some related works on wavelets and frames on ℚ , we refer to [3,16,18,19]. On the other hand, Lang [20][21][22] constructed several examples of compactly supported wavelets for the Cantor dyadic group.…”

mentioning

confidence: 99%

Affine, quasi-affine and co-affine frames on local fields of positive characteristic

Behera

Jahan

2017

Math. Nachr.

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Abstract. The concept of quasi-affine frame in Euclidean spaces was introduced to obtain translation invariance of the discrete wavelet transform. We extend this concept to a local field K of positive characteristic. We show that the affine system generated by a finite number of functions is an affine frame if and only the corresponding quasi-affine system is a quasi-affine frame. In such a case the exact frame bounds are equal. This result is obtained by using the properties of an operator associated with two such affine systems. We characterize the translation invariance of such an operator. A related concept is that of co-affine system. We show that there do not exist any co-affine frame in L 2 (K).

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p-Adic wavelets and their applications

Cited by 14 publications

References 76 publications

p-Adic mathematical physics: the first 30 years

p-Adic mathematical physics: the first 30 years

Wavelet Analysis on Symbolic Sequences and Two-Fold de Bruijn Sequences

Affine, quasi-affine and co-affine frames on local fields of positive characteristic

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