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pro vyhledávání: '"Doliwa, Adam"'
Autor:
Doliwa, Adam
We study multiple orthogonal polynomials exploiting their explicit determinantal representation in terms of moments. Our reasoning follows that applied to solve the Hermite-Pad\'{e} approximation and interpolation problems. We study also families of
Externí odkaz:
http://arxiv.org/abs/2312.15509
Hermite-Pad\'{e} approximation, multiple orthogonal polynomials, and multidimensional Toda equations
Autor:
Doliwa, Adam
We review recent results on the connection between Hermite-Pad\'e approximation problem, multiple orthogonal polynomials, and multidimensional Toda equations in continuous and discrete time. In order to motivate interest in the subject we first prese
Externí odkaz:
http://arxiv.org/abs/2310.15116
Autor:
Doliwa, Adam
Publikováno v:
Open Communications in Nonlinear Mathematical Physics, Special Issue in Memory of Decio Levi (February 15, 2024) ocnmp:12215
We present interpretation of known results in the theory of discrete asymptotic and discrete conjugate nets from the "discretization by B\"{a}cklund transformations" point of view. We collect both classical formulas of XIXth century differential geom
Externí odkaz:
http://arxiv.org/abs/2308.15959
Autor:
Doliwa, Adam, Siemaszko, Artur
We define quantization scheme for discrete-time random walks on the half-line consistent with Szegedy's quantization of finite Markov chains. Motivated by the Karlin and McGregor description of discrete-time random walks in terms of polynomials ortho
Externí odkaz:
http://arxiv.org/abs/2306.12265
Autor:
Doliwa, Adam
Publikováno v:
J. Phys. A: Math. Theor. 55 (2022) 505202 (17 pp.)
We study the interpolation analogue of the Hermite-Pad\'e type I approximation problem. We provide its determinant solution and we write down the corresponding integrable discrete system as an admissible reduction of Hirota's discrete Kadomtsev-Petvi
Externí odkaz:
http://arxiv.org/abs/2206.12502
Autor:
Doliwa, Adam
Publikováno v:
Lett. Math. Phys. 112 (2022) 68
We introduce and solve the non-commutative version of the Hermite-Pad\'{e} type I approximation problem. Its solution, expressed by quasideterminants, leads in a natural way to a subclass of solutions of the non-commutative Hirota (discrete Kadomtsev
Externí odkaz:
http://arxiv.org/abs/2202.00782
Autor:
Doliwa, Adam, Siemaszko, Artur
Publikováno v:
J. Approx. Theory 292 (2023) 105910 (23 pp.)
We show that solution to the Hermite-Pad\'{e} type I approximation problem leads in a natural way to a subclass of solutions of the Hirota (discrete Kadomtsev-Petviashvili) system and of its adjoint linear problem. Our result explains the appearence
Externí odkaz:
http://arxiv.org/abs/2201.06829
Autor:
Doliwa, Adam, Siemaszko, Artur
Publikováno v:
Numer. Algorithms 92 (2023) 571-596
We show that the Wynn recurrence (the missing identity of Frobenius of the Pad\'{e} approximation theory) can be incorporated into the theory of integrable systems as a reduction of the discrete Schwarzian Kadomtsev-Petviashvili equation. This allows
Externí odkaz:
http://arxiv.org/abs/2201.01749
Publikováno v:
J. Phys. A: Math. Theor. 54 (2021) 054001 (22 pp.)
The discrete non-commutative Darboux system of equations with self-consistent sources is constructed, utilizing both the vectorial fundamental (binary Darboux) transformation and the method of additional independent variables. Then the symmetric redu
Externí odkaz:
http://arxiv.org/abs/2010.16365
Autor:
Doliwa, Adam, Kashaev, Rinat M.
Publikováno v:
J. Math. Phys. 61 (2020) 092704 (23pp.)
We present new solutions of the functional Zamolodchikov tetrahedron equation in terms of birational maps in totally non-commutative variables. All the maps originate from Desargues lattices, which provide geometric realization of solutions to the no
Externí odkaz:
http://arxiv.org/abs/2005.11840