A. N. Kochubei, “Schrödinger-type operator over $p$-adic number field”, TMF, 86:3 (1991), 323–333; Theoret. and Math. Phys., 86:3 (1991), 221

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Teoreticheskaya i Matematicheskaya Fizika, 1991, Volume 86, Number 3, Pages 323–333 (Mi tmf5448)

This article is cited in 14 scientific papers (total in 14 papers)

Schrödinger-type operator over $p$-adic number field

A. N. Kochubei

Full-text PDF (1081 kB) Citations (14)

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Abstract: The spectral properties of a Schrödinger-type $p$-adic operator are studied. The self-adjointness of the minimal operator is proved. The completeness of the eigenvectors, the asymptotic behavior of the eigenvalues, and the position of the essential spectrum are considered.

Received: 24.08.1990

English version:
Theoretical and Mathematical Physics, 1991, Volume 86, Issue 3, Pages 221–228
DOI: https://doi.org/10.1007/BF01028417

Bibliographic databases:

Language: Russian

Citation: A. N. Kochubei, “Schrödinger-type operator over $p$-adic number field”, TMF, 86:3 (1991), 323–333; Theoret. and Math. Phys., 86:3 (1991), 221–228

Citation in format AMSBIB

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\paper Schr\"odinger-type operator over $p$-adic number field

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\transl

\jour Theoret. and Math. Phys.

\yr 1991

\vol 86

\issue 3

\pages 221--228

\crossref{https://doi.org/10.1007/BF01028417}

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Linking options:

https://www.mathnet.ru/eng/tmf5448

https://www.mathnet.ru/eng/tmf/v86/i3/p323

This publication is cited in the following 14 articles:

Ngo Thi Hong, Dao Van Duong, “Two-weighted estimates for p-adic Riesz potential and its commutators on Morrey–Herz spaces”, Fract Calc Appl Anal, 26:6 (2023), 2618
S. V. Kozyrev, A. Yu. Khrennikov, V. M. Shelkovich, “$p$-Adic wavelets and their applications”, Proc. Steklov Inst. Math., 285 (2014), 157–196
Khrennikov A.Yu. Kozyrev S.V. Oleschko K. Jaramillo A.G. de Jesus Correa Lopez M., “Application of P-Adic Analysis to Time Series”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 16:4 (2013), 1350030
A. Y. Khrennikov, V. M. Shelkovich, Jan Harm van der Walt, “Adelic Multiresolution Analysis, Construction of Wavelet Bases and Pseudo-Differential Operators”, J Fourier Anal Appl, 19:6 (2013), 1323
A. Y. Khrennikov, A. V. Kosyak, V. M. Shelkovich, “Wavelet Analysis on Adeles and Pseudo-Differential Operators”, J Fourier Anal Appl, 18:6 (2012), 1215
V. M. Shelkovich, “$p$-adic evolution pseudo-differential equations and $p$-adic wavelets”, Izv. Math., 75:6 (2011), 1249–1278
S. V. Kozyrev, “Methods and Applications of Ultrametric and $p$-Adic Analysis: From Wavelet Theory to Biophysics”, Proc. Steklov Inst. Math., 274, suppl. 1 (2011), S1–S84
Pseudo-Differential Equations And Stochastics Over Non-Archimedean Fields, 2001
Sergio Albeverio, Witold Karwowski, Xuelei Zhao, “Asymptotics and spectral results for random walks on p-adics”, Stochastic Processes and their Applications, 83:1 (1999), 39
V.S. Vladimirov, “Some problems of analysis on the field ofp-adic numbers”, Integral Transforms and Special Functions, 6:1-4 (1998), 111
A. N. Kochubei, “Gaussian integrals and spectral theory over a local field”, Russian Acad. Sci. Izv. Math., 45:3 (1995), 495–503
Sergio Albeverio, Witold Karwowski, “A random walk on p-adics—the generator and its spectrum”, Stochastic Processes and their Applications, 53:1 (1994), 1
A. N. Kochubei, “The differentiation operator on subsets of the field of $p$-adic numbers”, Russian Acad. Sci. Izv. Math., 41:2 (1993), 289–305
V. S. Vladimirov, “On spectral properties of $p$-adic pseudodifferential operators of Schrödinger type”, Russian Acad. Sci. Izv. Math., 41:1 (1993), 55–73

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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References:	92
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