On riemann 'nondifferentiable' function and Schrödinger equation

Autor: K. I. Oskolkov, M. A. Chakhkiev

Publikováno v: Proceedings of the Steklov Institute of Mathematics. 269:186-196

The function \( \psi : = \sum\nolimits_{n \in \mathbb{Z}\backslash \left\{ 0 \right\}} {{{e^{\pi i\left( {tn^2 + 2xn} \right)} } \mathord{\left/ {\vphantom {{e^{\pi i\left( {tn^2 + 2xn} \right)} } {\left( {\pi in^2 } \right)}}} \right. \kern-\nulldel

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::152392eb0c8d0bc97098c3268bfbd6d9
https://doi.org/10.1134/s0081543810020161

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Autor: K. I. Oskolkov

Publikováno v: Mathematical Notes. 74:232-244

In this paper, we prove a multiple analog of the theorem proved by Arkhipov and the author in 1987, which provides an estimate for the discrete Hilbert transform with polynomial phase. For the linear case, the corresponding estimates of the sum of mu

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::45e828b3efce2f1d33dfe7b3743f10d7
https://doi.org/10.1023/a:1025008308955

A note on orthonormal polynomial bases and wavelets

Autor: D. Offin, K. I. Oskolkov

Publikováno v: Constructive Approximation. 9:319-325

A simple and explicit construction of an orthnormal trigonometric polynomial basis in the spaceC of continuous periodic functions is presented. It consists simply of periodizing a well-known wavelet on the real line which is orthonormal and has compa

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::2017952f3d3e5ba497f1beb099cc312e
https://doi.org/10.1007/bf01198009

The Schrödinger density and the Talbot effect

Autor: K. I. Oskolkov

Publikováno v: Approximation and Probability.

We study the fractal properties of the time-dependent probability density function for the free quantum particle in a box, i.e. the squared magnitude of the solution of the Cauchy initial value problem for the Schrodinger equation with zero potential

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::5f3697a158cb5b39d4470006e5e944f8
https://doi.org/10.4064/bc72-0-13

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Autor: H. P. Barendregt, I. V. Dolgachev, G. Rozenberg, A. Salomaa, A. P. Soldatov, A. F. Leont’ev, V. F. Emel’yanov, I. P. Egorov, N. Kh. Rozov, V. V. Rumyantsev, I. B. Vapnyarskiĭ, L. D. Kudryavtsev, M. K. Samarin, I. V. Proskuryakov, V. M. Millionshchikov, N. N. Vil’yams, S. A. Stepanov, S. M. Voronin, I. V. Volovich, D. V. Anosov, D. D. Sokolov, P. K. Suetin, Yu. A. Brychkov, A. P. Prudnikov, A. B. Ivanov, M. I. Voĭtsekhovskiĭ, V. I. Bityutskov, V. A. Chuyanov, G. V. Kuz’mina, H. Maassen, E. D. Solomentsev, E. V. Shikin, A. V. Prokhorov, E. G. D’yakonov, M. V. Fedoryuk, M. A. Shubin, V. T. Bazylev, N. S. Zhavrid, V. V. Okhrimenko, Yu. M. Davydov, B. M. Bredikhin, V. V. Parail, V. I. Danilov, V. M. Mikheev, L. A. Skornyakov, N. G. Ushakov, V. M. Kopytov, T. S. Fofanova, V. A. Zorich, V. L. Popov, Yu. V. Prohorov, V. E. Plisko, V. V. Petrov, V. I. Nechaev, A. A. Bukhshtab, M. S. Nikulin, L. N. Bol’shev, K. I. Oskolkov, B. I. Golubov, V. V. Sazonov, P. S. Aleksandrov, B. S. Kashin, I. A. Vinogradova, B. A. Pasynkov, I. I. Volkov, T. P. Lukashenko, P. M. Gruber, Yu. B. Rudyak, V. A. Iskovskikh, Yu. V. Nesterenko, V. M. Tikhomirov, I. P. Mityuk, A. V. Chernavskiĭ, D. A. Ponomarev, E. G. Goluzina, Ü. Lumiste, A. I. Shtern, A. L. Onishchik, B. A. Rogozin, I. V. Ostrovskiĭ, V. M. Zolotarev, H. C. Myung, Yu. A. Bakhturin, E. B. Vinberg, A. A. Kirillov, V. V. Gorbatsevich, D. V. Alekseevskiĭ, V. P. Platonov, A. I. Kostrikin, A. S. Fedenko, B. R. Vaĭnberg, L. A. Cherkas, Yu. V. Prokhorov, A. I. Galochkin, A. S. Parkhomenko, V. V. Voevodin, A. F. Shapkin, S. G. Kreĭn, V. P. Palamodov, S. A. Aĭvazyan, A. Ya. Khelemskiĭ, A. M. Nakhushev, O. A. Ivanova, S. N. Chernikov, N. N. Ladis, V. G. Karmanov, V. A. Yakubovich, V. I. Arnautov, Yu. A. Rozanov, A. V. Malyshev, I. A. Kvasnikov, A. F. Lavrik, S. V. Kotov, I. Kh. Sabitov, A. V. Efimov, A. P. Ershov, M. Sh. Farber, B. L. Laptev, Kh. D. Ikramov, L. A. Sidorov, I. P. Mysovskikh, N. P. Koreneĭchuk, V. P. Motornyĭ, A. A. Mal’tsev, E. G. Sklyarenko, L. V. Kuz’min, P. T. Johnstone, A. A. Dezin, M. Sh. Tsalenko, A. I. Untern, V. N. Latyshev, A. V. Arkhangel’skiĭ, A. L. Shmel’kin, L. N. Shevrin, S. A. Bogatyĭ, S. Yu. Maslov, G. E. Mints, A. I. Orlov, V. D. Belousov, A. F. Kharshiladze, V. Ya. Gutlyanskiĭ, E. M. Semenov, A. A. Konyushkov, B. A. Efimov, R. Z. Khas’minskiĭ, N. M. Nagornyĭ, V. V. Fedorchuk, B. V. Khvedelidze

Publikováno v: Encyclopaedia of Mathematics ISBN: 9780792329756

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::91346d0ea5889d49a1cf9df9414cae75
https://doi.org/10.1007/978-1-4899-3793-3_5