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Izv. RAN. Ser. Mat., 2002, Volume 66, Issue 2, Pages 149–158 (Mi izv381)  

This article is cited in 100 scientific papers (total in 100 papers)

Wavelet theory as $p$-adic spectral analysis

S. V. Kozyrev


Abstract: We construct a new orthonormal basis of eigenfunctions of the Vladimirov $p$-adic fractional differentiation operator. We construct a map of the $p$-adic numbers onto the real numbers (the $p$-adic change of variables), which transforms the Haar measure on the $p$-adic numbers to the Lebesgue measure on the positive semi-axis. The $p$-adic change of variables (for $p=2$) provides an equivalence between the basis of eigenfunctions of the Vladimirov operator and the wavelet basis in $L^2({\mathbb R}_+)$ generated by the Haar wavelet. This means that wavelet theory can be regarded as $p$-adic spectral analysis.

DOI: https://doi.org/10.4213/im381

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English version:
Izvestiya: Mathematics, 2002, 66:2, 367–376

Bibliographic databases:

Document Type: Article
UDC: 517.58+517.53.02
MSC: 26E30, 46S10
Received: 23.02.2001

Citation: S. V. Kozyrev, “Wavelet theory as $p$-adic spectral analysis”, Izv. RAN. Ser. Mat., 66:2 (2002), 149–158; Izv. Math., 66:2 (2002), 367–376

Citation in format AMSBIB
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\by S.~V.~Kozyrev
\paper Wavelet theory as $p$-adic spectral analysis
\jour Izv. RAN. Ser. Mat.
\yr 2002
\vol 66
\issue 2
\pages 149--158
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\transl
\jour Izv. Math.
\yr 2002
\vol 66
\issue 2
\pages 367--376
\crossref{https://doi.org/10.1070/IM2002v066n02ABEH000381}
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  • https://doi.org/10.4213/im381
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    This publication is cited in the following articles:
    1. S. V. Kozyrev, “Rigged Hilbert Space of Free Coherent States and $p$-Adic Numbers”, Theoret. and Math. Phys., 135:2 (2003), 642–650  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. V. S. Vladimirov, “Tables of Integrals of Complex-Valued Functions of $p$-Adic Arguments”, Proc. Steklov Inst. Math., 284, suppl. 2 (2014), S1–S59  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Proc. Steklov Inst. Math., 245 (2004), 34–39  mathnet  mathscinet  zmath
    4. S. V. Kozyrev, “$p$-Adic Pseudodifferential Operators: Methods and Applications”, Proc. Steklov Inst. Math., 245 (2004), 143–153  mathnet  mathscinet  zmath
    5. S. V. Kozyrev, “$p$-Adic Pseudodifferential Operators and $p$-Adic Wavelets”, Theoret. and Math. Phys., 138:3 (2004), 322–332  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. Benedetto J.J., Benedetto R.L., “A wavelet theory for local fields and related groups”, J. Geom. Anal., 14:3 (2004), 423–456  crossref  mathscinet  zmath  isi  scopus
    7. A. Yu. Khrennikov, S. V. Kozyrev, “$p$-Adic Pseudodifferential Operators and Analytic Continuation of Replica Matrices”, Theoret. and Math. Phys., 144:2 (2005), 1166–1170  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. Kozyrev S.V., Osipov V.Al., Avetisov V.A., “Nondegenerate ultrametric diffusion”, J. Math. Phys., 46:6 (2005), 063302, 15 pp.  crossref  mathscinet  zmath  adsnasa  isi  scopus
    9. Yu. A. Farkov, “Orthogonal wavelets with compact support on locally compact Abelian groups”, Izv. Math., 69:3 (2005), 623–650  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    10. S. V. Kozyrev, A. Yu. Khrennikov, “Pseudodifferential operators on ultrametric spaces and ultrametric wavelets”, Izv. Math., 69:5 (2005), 989–1003  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    11. Khrennikov A.Yu., Kozyrev S.V., “Wavelets on ultrametric spaces”, Appl. Comput. Harmon. Anal., 19:1 (2005), 61–76  crossref  mathscinet  zmath  isi  elib  scopus
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    14. Khrennikov A.Yu., Shelkovich V.M., “Distributional asymptotics and $p$-adic Tauberian and Shannon-Kotelnikov theorems”, Asymptot. Anal., 46:2 (2006), 163–187  mathscinet  zmath  isi  elib
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    17. Khrennikov A.Yu., Kozyrev S.V., “Replica symmetry breaking related to a general ultrametric space — II: RSB solutions and the $n\to 0$ limit”, Physica A: Statistical Mechanics and its Applications, 359 (2006), 241–266  crossref  adsnasa  isi  scopus
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    25. Tarakanov A.O., “Immunocomputing for intelligent intrusion detection”, IEEE Computational Intelligence Magazine, 3:2 (2008), 22–30  crossref  isi  elib  scopus
    26. Khrennikov A.Yu., Shelkovich V.M., “Non-haar $p$-adic wavelets and pseudodifferential operators”, Dokl. Math., 77:1 (2008), 42–45  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    27. Albeverio S., Kuzhel S., Torba S., “$p$-adic Schrödinger-type operator with point interactions”, J. Math. Anal. Appl., 338:2 (2008), 1267–1281  crossref  mathscinet  zmath  isi  elib  scopus
    28. Chuong Nguyen Minh, Co Nguyen Van, “The Cauchy problem for a class of pseudodifferential equations over $p$-adic field”, J. Math. Anal. Appl., 340:1 (2008), 629–645  crossref  mathscinet  zmath  isi  elib  scopus
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    30. Chuong N.M., Van Co N., “P-adic pseudodifferential operators and wavelets”, Frames and Operator Theory in Analysis and Signal Processing, Contemporary Mathematics Series, 451, 2008, 33–45  crossref  mathscinet  zmath  isi
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    33. Proc. Steklov Inst. Math., 265 (2009), 1–12  mathnet  crossref  mathscinet  zmath  isi  elib
    34. Proc. Steklov Inst. Math., 265 (2009), 13–29  mathnet  crossref  mathscinet  zmath  isi  elib
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    39. Farkov Yu.A., “On wavelets related to the Walsh series”, J. Approx. Theory, 161:1 (2009), 259–279  crossref  mathscinet  zmath  isi  elib  scopus
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    51. Kigami J., “Dirichlet forms and associated heat kernels on the Cantor set induced by random walks on trees”, Advances in Mathematics, 225:5 (2010), 2674–2730  crossref  mathscinet  zmath  isi  scopus
    52. Albeverio S., Evdokimov S., Skopina M., “p-Adic Multiresolution Analysis and Wavelet Frames”, Journal of Fourier Analysis and Applications, 16:5 (2010), 693–714  crossref  mathscinet  zmath  isi  elib  scopus
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    54. Sergei F. Lukomskii, “Haar system on a product of zero-dimensional compact groups”, Centr. Eur. J. Math., 9:3 (2011), 627–639  crossref  mathscinet  zmath  isi  scopus
    55. S. F. Lukomskii, “Neortogonalnyi kratnomasshtabnyi analiz na nul-mernykh lokalno kompaktnykh gruppakh”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 11:3(1) (2011), 25–32  mathnet  elib
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    57. S. F. Lukomskii, “Haar System on the Product of Groups of $p$-Adic Integers”, Math. Notes, 90:4 (2011), 517–532  mathnet  crossref  crossref  mathscinet  isi
    58. V. M. Shelkovich, “$p$-adic evolution pseudo-differential equations and $p$-adic wavelets”, Izv. Math., 75:6 (2011), 1249–1278  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    59. Kopaliani T., “Higher rank Haar wavelet bases in spaces L-w(p)(R)”, Georgian Math J, 18:3 (2011), 517–532  mathscinet  zmath  isi  elib
    60. Jorgensen P.E.T., Pearse E.P.J., “Resistance Boundaries of Infinite Networks”, Random Walks, Boundaries and Spectra, Progress in Probability, 64, eds. Lenz D., Sobieczky F., Woess W., Birkhauser Verlag Ag, 2011, 111–142  mathscinet  zmath  isi
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    62. Lukomskii S.F., “Multiresolution analysis on product of zero-dimensional Abelian groups”, J Math Anal Appl, 385:2 (2012), 1162–1178  crossref  mathscinet  zmath  isi  elib  scopus
    63. I. Ya. Novikov, M. A. Skopina, “Why Are Haar Bases in Various Structures the Same?”, Math. Notes, 91:6 (2012), 895–898  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    64. Khrennikov A.Y. Kosyak A.V. Shelkovich V.M., “Wavelet Analysis on Adeles and Pseudo-Differential Operators”, J. Fourier Anal. Appl., 18:6 (2012), 1215–1264  crossref  mathscinet  zmath  isi  scopus
    65. Behera B., Jahan Q., “Wavelet Packets and Wavelet Frame Packets on Local Fields of Positive Characteristic”, J. Math. Anal. Appl., 395:1 (2012), 1–14  crossref  mathscinet  zmath  isi  elib  scopus
    66. Albeverio S., Skopina M., “Haar Bases for l-2(Q(2)(2)) Generated by One Wavelet Function”, Int. J. Wavelets Multiresolut. Inf. Process., 10:5 (2012), 1250042  crossref  mathscinet  zmath  isi  elib  scopus
    67. Kosyak A.V., Khrennikov A.Yu., Shelkovich V.M., “Wavelet Bases on Adele Rings”, Dokl. Math., 85:1 (2012), 75–79  crossref  mathscinet  zmath  isi  elib  elib  scopus
    68. Kosyak A.V., Khrennikov A.Yu., Shelkovich V.M., “Pseudodifferential Operators on Adele Rings and Wavelet Bases”, Dokl. Math., 85:3 (2012), 358–362  crossref  mathscinet  zmath  isi  elib  elib  scopus
    69. S. Evdokimov, “Haar multiresolution analysis and Haar bases on the ring of rational adeles”, J. Math. Sci. (N. Y.), 192:2 (2013), 215–219  mathnet  crossref  mathscinet
    70. A. YU. KHRENNIKOV, S. V. KOZYREV, K. OLESCHKO, A. G. JARAMILLO, M. de JESÚS CORREA LÓPEZ, “APPLICATION OF p-ADIC ANALYSIS TO TIME SERIES”, Infin. Dimens. Anal. Quantum. Probab. Relat. Top, 16:04 (2013), 1350030  crossref  mathscinet  zmath  isi  scopus
    71. King E.J., “Frame Theory for Locally Compact Abelian Groups”, Wavelets and Sparsity XV, Proceedings of SPIE, 8858, eds. VanDeVille D., Goyal V., Papadakis M., SPIE-Int Soc Optical Engineering, 2013, 88581R  crossref  isi  scopus
    72. Khrennikov A.Y., Shelkovich V.M., van der Walt J.H., “Adelic Multiresolution Analysis, Construction of Wavelet Bases and Pseudo-Differential Operators”, J. Fourier Anal. Appl., 19:6 (2013), 1323–1358  crossref  mathscinet  zmath  isi  scopus
    73. S. V. Kozyrev, A. Yu. Khrennikov, V. M. Shelkovich, “$p$-Adic wavelets and their applications”, Proc. Steklov Inst. Math., 285 (2014), 157–196  mathnet  crossref  crossref  isi
    74. Yu. S. Kruss, “Ob operatore differentsirovaniya na kompaktnykh nul-mernykh gruppakh”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 14:3 (2014), 279–287  mathnet
    75. A. A. Baryshev, D. S. Lukomskii, S. F. Lukomskii, “Sistemy szhatii i sdvigov v zadache szhatiya izobrazhenii”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 14:4(2) (2014), 505–510  mathnet
    76. Lukomskii S.F., “Step Refinable Functions and Orthogonal Mra on Vilenkin Groups”, J. Fourier Anal. Appl., 20:1 (2014), 42–65  crossref  mathscinet  zmath  isi  scopus
    77. S. F. Lukomskii, “Riesz multiresolution analysis on zero-dimensional groups”, Izv. Math., 79:1 (2015), 145–176  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    78. Evdokimov S., Skopina M., “On Orthogonal P-Adic Wavelet Bases”, J. Math. Anal. Appl., 424:2 (2015), 952–965  crossref  mathscinet  zmath  isi  scopus
    79. Shukla N.K. Vyas A., “Multiresolution Analysis Through Low-Pass Filter on Local Fields of Positive Characteristic”, Complex Anal. Oper. Theory, 9:3 (2015), 631–652  crossref  mathscinet  zmath  isi  scopus
    80. Khrennikov A., Kozyrev S., Mansson A., “Hierarchical Model of the Actomyosin Molecular Motor Based on Ultrametric Diffusion With Drift”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 18:2 (2015), 1550013  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    81. Goyal S., Shah F.A., “Construction of Periodic Wavelet Frames Generated by the Walsh Polynomials”, 3, no. 4, 2015, 1171–1191  crossref  mathscinet  zmath  isi
    82. Lukomskii S.F. Vodolazov A.M., “Non-Haar Mra on Local Fields of Positive Characteristic”, J. Math. Anal. Appl., 433:2 (2016), 1415–1440  crossref  mathscinet  zmath  isi  elib  scopus
    83. Evdokimov S., “On non-compactly supported p-adic wavelets”, J. Math. Anal. Appl., 443:2 (2016), 1260–1266  crossref  mathscinet  zmath  isi  elib  scopus
    84. Khrennikov A., Oleschko K., Correa Lopez Maria de Jess, “Application of p-Adic Wavelets to Model Reaction–Diffusion Dynamics in Random Porous Media”, J. Fourier Anal. Appl., 22:4 (2016), 809–822  crossref  mathscinet  zmath  isi  elib  scopus
    85. Khrennikov A. Oleschko K. Correa Lopez Maria de Jesus, “Modeling Fluid's Dynamics with Master Equations in Ultrametric Spaces Representing the Treelike Structure of Capillary Networks”, Entropy, 18:7 (2016), 249  crossref  mathscinet  isi  scopus
    86. Al Osipov V., “Wavelet Analysis on Symbolic Sequences and Two-Fold de Bruijn Sequences”, J. Stat. Phys., 164:1 (2016), 142–165  crossref  mathscinet  zmath  isi  elib  scopus
    87. Li Y., Qiu H., Nonlinear Anal.-Theory Methods Appl., 139 (2016), 131–151  crossref  mathscinet  zmath  isi  scopus
    88. Actis M., Aimar H., Bongioanni B., Gomez I., “Nonlocal Schrödinger equations in metric measure spaces”, J. Math. Anal. Appl., 435:1 (2016), 425–439  crossref  mathscinet  zmath  isi  scopus
    89. A. Kh. Bikulov, A. P. Zubarev, “Polnye sistemy sobstvennykh funktsii operatora Vladimirova v $L^{2}(B_r)$ i $L^{2}(\mathbb{Q}_{p})$”, Fundament. i prikl. matem., 21:3 (2016), 39–56  mathnet
    90. K. Oleschko, A. Yu. Khrennikov, “Applications of $p$-adics to geophysics: Linear and quasilinear diffusion of water-in-oil and oil-in-water emulsions”, Theoret. and Math. Phys., 190:1 (2017), 154–163  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    91. St. Petersburg Math. J., 29:3 (2018), 529–544  mathnet  crossref  isi  elib
    92. A. M. Vodolazov, S. F. Lukomskii, “Cistemy sdvigov v lokalnykh polyakh nulevoi kharakteristiki”, Voprosy teorii predstavlenii algebr i grupp. 31, Zap. nauchn. sem. POMI, 455, POMI, SPb., 2017, 25–32  mathnet
    93. E. Dzh. King, M. A. Skopina, “O biortogonalnykh $p$-adicheskikh bazisakh vspleskov”, Voprosy teorii predstavlenii algebr i grupp. 31, Zap. nauchn. sem. POMI, 455, POMI, SPb., 2017, 67–83  mathnet
    94. Oleschko K. Khrennikov A., “Transport Through a Network of Capillaries From Ultrametric Diffusion Equation With Quadratic Nonlinearity”, Russ. J. Math. Phys., 24:4 (2017), 505–516  crossref  mathscinet  zmath  isi  scopus
    95. Dragovich B. Khrennikov A.Yu. Kozyrev S.V. Volovich I.V. Zelenov E.I., “P-Adic Mathematical Physics: the First 30 Years”, P-Adic Numbers Ultrametric Anal. Appl., 9:2 (2017), 87–121  crossref  mathscinet  zmath  isi  scopus
    96. Nguyen Minh Chuong, Nguyen Thi Hong, Ha Duy Hung, “Bounds of Weighted Multilinear Hardy-Cesa Ro Operators in P-Adic Functional Spaces”, Front. Math. China, 13:1 (2018), 1–24  crossref  mathscinet  zmath  isi  scopus
    97. Pathak A., Singh G.P., “Wavelets in Sobolev Space Over Local Fields of Positive Characteristics”, Int. J. Wavelets Multiresolut. Inf. Process., 16:4 (2018), 1850027  crossref  mathscinet  zmath  isi  scopus
    98. Saberi I., “Holography and Local Fields”, P-Adic Numbers Ultrametric Anal. Appl., 10:3 (2018), 151–165  crossref  mathscinet  isi  scopus
    99. Antoniouk V A., Oleschko K., Kochubei A.N., Khrennikov A.Yu., “A Stochastic P-Adic Model of the Capillary Flow in Porous Random Medium”, Physica A, 505 (2018), 763–777  crossref  mathscinet  isi  scopus
    100. K. S. Kazarian, A. San Antolin, “Wavelets and Bidemocratic Pairs in Weighted Norm Spaces”, Math. Notes, 104:4 (2018), 508–517  mathnet  crossref  crossref  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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