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Вадим Борзов

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Papers by Вадим Борзов

Research paper thumbnail of Crazy states: a counterconventional strategic problem

Kraus Reprint, Millwood, NY, 1980

... Crazy states: A counterconventional strategic problem. Post a Comment. CONTRIBUTORS: Author: ... more ... Crazy states: A counterconventional strategic problem. Post a Comment. CONTRIBUTORS: Author: Dror, Yehezkel (b. 1928, d. ----. PUBLISHER: Kraus Reprint (Millwood, NY). SERIES TITLE: YEAR: 1980. PUB TYPE: Book (ISBN 0527251402 ). VOLUME/EDITION: ...

Research paper thumbnail of Compound model of the generalized oscillator. I

Journal of Mathematical Sciences, 2010

We study the problem of realization of a given generalized oscillator by a system of N generalize... more We study the problem of realization of a given generalized oscillator by a system of N generalized oscillators of a different type. We consider a generalized oscillator related to a fixed system of orthogonal polynomials that are determined by three-term recurrent relations and the corresponding three-diagonal Jacobi matrix J. The case N = 2 was considered in a previous paper. It was shown that in this case the orthogonality measure is symmetric with respect to rotation at angle π. In this paper, we consider the case N = 3. We prove that such a problem has a solution only in two cases. In the first case, the Jacobi matrix related to the given "composite" generalized oscillator has block-diagonal form and consists of similar 3×3 blocks. In the second (more interesting) possible case, the Jacobi matrix is not block-diagonal. For this matrix, we construct the corresponding system of orthogonal polynomials. This system decomposes into three series which are related to Chebyshev polynomials of the second kind. The main result of the paper is a solution of the moment problem for the corresponding Jacobi matrix. In this case, the constructed measure is symmetric with respect to rotation at angle 2π/3. Bibliography: 6 titles.

Research paper thumbnail of Локальное возмущение дискретного уравнения Шредингера и обобщенный осциллятор Чебышeва

Teoreticheskaya i Matematicheskaya Fizika

На примере дискретного уравнения Шредингера обсуждаются условия, при которых специальные линейные... more На примере дискретного уравнения Шредингера обсуждаются условия, при которых специальные линейные преобразования классических многочленов Чебышeва (2-го рода) порождают класс многочленов, связанных с…

Research paper thumbnail of Инвариантность обобщенного осциллятора относительно линейного преобразования соответствующей системы ортогональных полиномов

Teoreticheskaya i Matematicheskaya Fizika

Research paper thumbnail of Обобщенный осциллятор и его когерентные состояния

Теоретическая и математическая физика, 2007

Research paper thumbnail of Ортогональные многочлены и деформированные осцилляторы

Теоретическая и математическая физика, 2015

Research paper thumbnail of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>N</mi></mrow><annotation encoding="application/x-tex">N</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">N</span></span></span></span>-симметричные полиномы Чебышева в составной модели обобщенного осциллятора

Теоретическая и математическая физика, 2011

Research paper thumbnail of Обобщенные когерентные состояния для осцилляторов, связанных с <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>q</mi></mrow><annotation encoding="application/x-tex">q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span></span></span></span>-полиномами Шарлье

Теоретическая и математическая физика, 2008

Research paper thumbnail of Compound model of the generalized oscillator. I

Journal of Mathematical Sciences, 2010

We study the problem of realization of a given generalized oscillator by a system of N generalize... more We study the problem of realization of a given generalized oscillator by a system of N generalized oscillators of a different type. We consider a generalized oscillator related to a fixed system of orthogonal polynomials that are determined by three-term recurrent relations and the corresponding three-diagonal Jacobi matrix J. The case N = 2 was considered in a previous paper. It was shown that in this case the orthogonality measure is symmetric with respect to rotation at angle π. In this paper, we consider the case N = 3. We prove that such a problem has a solution only in two cases. In the first case, the Jacobi matrix related to the given "composite" generalized oscillator has block-diagonal form and consists of similar 3×3 blocks. In the second (more interesting) possible case, the Jacobi matrix is not block-diagonal. For this matrix, we construct the corresponding system of orthogonal polynomials. This system decomposes into three series which are related to Chebyshev polynomials of the second kind. The main result of the paper is a solution of the moment problem for the corresponding Jacobi matrix. In this case, the constructed measure is symmetric with respect to rotation at angle 2π/3. Bibliography: 6 titles.

Research paper thumbnail of Crazy states: a counterconventional strategic problem

Kraus Reprint, Millwood, NY, 1980

... Crazy states: A counterconventional strategic problem. Post a Comment. CONTRIBUTORS: Author: ... more ... Crazy states: A counterconventional strategic problem. Post a Comment. CONTRIBUTORS: Author: Dror, Yehezkel (b. 1928, d. ----. PUBLISHER: Kraus Reprint (Millwood, NY). SERIES TITLE: YEAR: 1980. PUB TYPE: Book (ISBN 0527251402 ). VOLUME/EDITION: ...

Research paper thumbnail of Compound model of the generalized oscillator. I

Journal of Mathematical Sciences, 2010

We study the problem of realization of a given generalized oscillator by a system of N generalize... more We study the problem of realization of a given generalized oscillator by a system of N generalized oscillators of a different type. We consider a generalized oscillator related to a fixed system of orthogonal polynomials that are determined by three-term recurrent relations and the corresponding three-diagonal Jacobi matrix J. The case N = 2 was considered in a previous paper. It was shown that in this case the orthogonality measure is symmetric with respect to rotation at angle π. In this paper, we consider the case N = 3. We prove that such a problem has a solution only in two cases. In the first case, the Jacobi matrix related to the given "composite" generalized oscillator has block-diagonal form and consists of similar 3×3 blocks. In the second (more interesting) possible case, the Jacobi matrix is not block-diagonal. For this matrix, we construct the corresponding system of orthogonal polynomials. This system decomposes into three series which are related to Chebyshev polynomials of the second kind. The main result of the paper is a solution of the moment problem for the corresponding Jacobi matrix. In this case, the constructed measure is symmetric with respect to rotation at angle 2π/3. Bibliography: 6 titles.

Research paper thumbnail of Локальное возмущение дискретного уравнения Шредингера и обобщенный осциллятор Чебышeва

Teoreticheskaya i Matematicheskaya Fizika

На примере дискретного уравнения Шредингера обсуждаются условия, при которых специальные линейные... more На примере дискретного уравнения Шредингера обсуждаются условия, при которых специальные линейные преобразования классических многочленов Чебышeва (2-го рода) порождают класс многочленов, связанных с…

Research paper thumbnail of Инвариантность обобщенного осциллятора относительно линейного преобразования соответствующей системы ортогональных полиномов

Teoreticheskaya i Matematicheskaya Fizika

Research paper thumbnail of Обобщенный осциллятор и его когерентные состояния

Теоретическая и математическая физика, 2007

Research paper thumbnail of Ортогональные многочлены и деформированные осцилляторы

Теоретическая и математическая физика, 2015

Research paper thumbnail of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>N</mi></mrow><annotation encoding="application/x-tex">N</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">N</span></span></span></span>-симметричные полиномы Чебышева в составной модели обобщенного осциллятора

Теоретическая и математическая физика, 2011

Research paper thumbnail of Обобщенные когерентные состояния для осцилляторов, связанных с <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>q</mi></mrow><annotation encoding="application/x-tex">q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span></span></span></span>-полиномами Шарлье

Теоретическая и математическая физика, 2008

Research paper thumbnail of Compound model of the generalized oscillator. I

Journal of Mathematical Sciences, 2010

We study the problem of realization of a given generalized oscillator by a system of N generalize... more We study the problem of realization of a given generalized oscillator by a system of N generalized oscillators of a different type. We consider a generalized oscillator related to a fixed system of orthogonal polynomials that are determined by three-term recurrent relations and the corresponding three-diagonal Jacobi matrix J. The case N = 2 was considered in a previous paper. It was shown that in this case the orthogonality measure is symmetric with respect to rotation at angle π. In this paper, we consider the case N = 3. We prove that such a problem has a solution only in two cases. In the first case, the Jacobi matrix related to the given "composite" generalized oscillator has block-diagonal form and consists of similar 3×3 blocks. In the second (more interesting) possible case, the Jacobi matrix is not block-diagonal. For this matrix, we construct the corresponding system of orthogonal polynomials. This system decomposes into three series which are related to Chebyshev polynomials of the second kind. The main result of the paper is a solution of the moment problem for the corresponding Jacobi matrix. In this case, the constructed measure is symmetric with respect to rotation at angle 2π/3. Bibliography: 6 titles.

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