Alexis, Michel; Aptekarev, Alexander; Denisov, Sergey Continuity of weighted operators, Muckenhoupt \(A_p\) weights, and Steklov problem for orthogonal polynomials. (English) Zbl 1487.42059 Int. Math. Res. Not. 2022, No. 8, 5935-5972 (2022). MSC: 42C05 42B30 47B38 PDFBibTeX XMLCite \textit{M. Alexis} et al., Int. Math. Res. Not. 2022, No. 8, 5935--5972 (2022; Zbl 1487.42059) Full Text: DOI arXiv
Aptekarev, Alexander I.; Dobrokhotov, Sergey Yu.; Tulyakov, Dmitrii N.; Tsvetkova, Anna V. Plancherel-Rotach type asymptotic formulae for multiple orthogonal Hermite polynomials and recurrence relations. (English. Russian original) Zbl 1510.33008 Izv. Math. 86, No. 1, 32-91 (2022); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 86, No. 1, 36-97 (2022). MSC: 33C45 33C10 39A06 42C05 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., Izv. Math. 86, No. 1, 32--91 (2022; Zbl 1510.33008); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 86, No. 1, 36--97 (2022) Full Text: DOI
Aptekarev, Alexander I.; Denisov, Sergey A.; Yattselev, Maxim L. On spectrum of a class of Jacobi matrices on graph-trees and multiple orthogonal polynomials. (English) Zbl 1503.33009 Abakumov, Evgeny (ed.) et al., Extended abstracts fall 2019. Spaces of analytic functions: approximation, interpolation, sampling, SAFAIS 2019 program, Centre de Recerca Matemàtica, Barcelona, Spain, October–December 2019. Cham: Birkhäuser. Trends Math., Res. Perspect. CRM Barc. 12, 17-24 (2021). MSC: 33C45 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., Trends Math., Res. Perspect. CRM Barc. 12, 17--24 (2021; Zbl 1503.33009) Full Text: DOI
Aptekarev, Alexander I.; Denisov, Sergey A.; Yattselev, Maxim L. Jacobi matrices on trees generated by Angelesco systems: asymptotics of coefficients and essential spectrum. (English) Zbl 1501.47050 J. Spectr. Theory 11, No. 4, 1511-1597 (2021). MSC: 47B36 47A10 42C05 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., J. Spectr. Theory 11, No. 4, 1511--1597 (2021; Zbl 1501.47050) Full Text: DOI arXiv
Aptekarev, A. I.; Denisov, S. A.; Yattselev, M. L. Discrete Schrödinger operator on a tree, Angelesco potentials, and their perturbations. (English. Russian original) Zbl 1458.39015 Proc. Steklov Inst. Math. 311, 1-9 (2020); translation from Tr. Mat. Inst. Steklova 311, 5-13 (2020). MSC: 39A70 39A12 37E25 34L40 33C45 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., Proc. Steklov Inst. Math. 311, 1--9 (2020; Zbl 1458.39015); translation from Tr. Mat. Inst. Steklova 311, 5--13 (2020) Full Text: DOI
Aptekarev, Alexander I.; Kozhan, Rostyslav Differential equations for the recurrence coefficients limits for multiple orthogonal polynomials from a Nevai class. (English) Zbl 1440.42115 J. Approx. Theory 255, Article ID 105409, 20 p. (2020). MSC: 42C05 33C45 34A05 PDFBibTeX XMLCite \textit{A. I. Aptekarev} and \textit{R. Kozhan}, J. Approx. Theory 255, Article ID 105409, 20 p. (2020; Zbl 1440.42115) Full Text: DOI arXiv
Aptekarev, Alexander I.; Denisov, Sergey A.; Yattselev, Maxim L. Self-adjoint Jacobi matrices on trees and multiple orthogonal polynomials. (English) Zbl 1433.42027 Trans. Am. Math. Soc. 373, No. 2, 875-917 (2020). MSC: 42C05 47B36 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., Trans. Am. Math. Soc. 373, No. 2, 875--917 (2020; Zbl 1433.42027) Full Text: DOI arXiv
Aptekarev, Aleksandr I.; Belega, Elena D. Asymptotic behaviour of the information entropy of hydrogen-like quantum systems. (English. Russian original) Zbl 1425.81025 Russ. Math. Surv. 73, No. 5, 922-924 (2018); translation from Usp. Mat. Nauk 73, No. 5, 185-186 (2018). MSC: 81Q05 81S05 94A17 81P45 33C45 35P20 PDFBibTeX XMLCite \textit{A. I. Aptekarev} and \textit{E. D. Belega}, Russ. Math. Surv. 73, No. 5, 922--924 (2018; Zbl 1425.81025); translation from Usp. Mat. Nauk 73, No. 5, 185--186 (2018) Full Text: DOI
Aptekarev, A. I.; Draux, A.; Tulyakov, D. N. On asymptotics of the sharp constants of the Markov-Bernshtein inequalities for the Sobolev spaces. (English) Zbl 1400.41022 Lobachevskii J. Math. 39, No. 5, 609-622 (2018). MSC: 41A44 26D05 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., Lobachevskii J. Math. 39, No. 5, 609--622 (2018; Zbl 1400.41022) Full Text: DOI
Aptekarev, A. I.; López Lagomasino, G.; Martínez-Finkelshtein, A. On Nikishin systems with discrete components and weak asymptotics of multiple orthogonal polynomials. (English. Russian original) Zbl 1379.42011 Russ. Math. Surv. 72, No. 3, 389-449 (2017); translation from Usp. Mat. Nauk 72, No. 3, 3-64 (2017). Reviewer: Marcel G. de Bruin (Heemstede) MSC: 42C05 31A99 41A21 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., Russ. Math. Surv. 72, No. 3, 389--449 (2017; Zbl 1379.42011); translation from Usp. Mat. Nauk 72, No. 3, 3--64 (2017) Full Text: DOI arXiv
Aptekarev, A. I. The Mhaskar-Saff variational principle and location of the shocks’ of certain hyperbolic equations. (English) Zbl 1350.41012 Hardin, Douglas P. (ed.) et al., Modern trends in constructive function theory. Constructive functions 2014 conference in honor of Ed Saff’s 70th birthday, Vanderbilt University, Nashville, TN, USA, May 26–30, 2014. Proceedings. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-2534-0/pbk; 978-1-4704-2934-8/ebook). Contemporary Mathematics 661, 167-186 (2016). MSC: 41A20 41A21 41A10 PDFBibTeX XMLCite \textit{A. I. Aptekarev}, Contemp. Math. 661, 167--186 (2016; Zbl 1350.41012) Full Text: DOI
Aptekarev, A.; Denisov, S.; Tulyakov, D. On a problem by Steklov. (English) Zbl 1348.42024 J. Am. Math. Soc. 29, No. 4, 1117-1165 (2016). Reviewer: Edmundo J. Huertas (Madrid) MSC: 42C05 33D45 PDFBibTeX XMLCite \textit{A. Aptekarev} et al., J. Am. Math. Soc. 29, No. 4, 1117--1165 (2016; Zbl 1348.42024) Full Text: DOI arXiv
Aptekarev, Alexander I.; Derevyagin, Maxim; Miki, Hiroshi; Van Assche, Walter Multidimensional Toda lattices: continuous and discrete time. (English) Zbl 1341.42042 SIGMA, Symmetry Integrability Geom. Methods Appl. 12, Paper 054, 30 p. (2016). Reviewer: Ma Wen-Xiu (Tampa) MSC: 42C05 37K10 39A14 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 12, Paper 054, 30 p. (2016; Zbl 1341.42042) Full Text: DOI arXiv
Aptekarev, Alexander I.; Derevyagin, Maxim; van Assche, Walter Discrete integrable systems generated by Hermite-Padé approximants. (English) Zbl 1341.42043 Nonlinearity 29, No. 5, 1487-1506 (2016). Reviewer: Marcel G. de Bruin (Haarlem) MSC: 42C05 37K10 37K60 39A12 65Q10 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., Nonlinearity 29, No. 5, 1487--1506 (2016; Zbl 1341.42043) Full Text: DOI arXiv
Aptekarev, A. I.; Geronimo, J. S. Measures for orthogonal polynomials with unbounded recurrence coefficients. (English) Zbl 1343.42037 J. Approx. Theory 207, 339-347 (2016). Reviewer: M. Abdessadek Saib (Tebessa) MSC: 42C05 41A60 PDFBibTeX XMLCite \textit{A. I. Aptekarev} and \textit{J. S. Geronimo}, J. Approx. Theory 207, 339--347 (2016; Zbl 1343.42037) Full Text: DOI arXiv
Aptekarev, A. I.; Tulyakov, D. N. Asymptotics of \(L_p\)-norms of Laguerre polynomials. (English. Russian original) Zbl 1346.42030 Russ. Math. Surv. 70, No. 5, 955-957 (2015); translation from Usp. Mat. Nauk 70, No. 5, 177-178 (2015). Reviewer: Pierluigi Vellucci (Roma) MSC: 42C05 94A17 PDFBibTeX XMLCite \textit{A. I. Aptekarev} and \textit{D. N. Tulyakov}, Russ. Math. Surv. 70, No. 5, 955--957 (2015; Zbl 1346.42030); translation from Usp. Mat. Nauk 70, No. 5, 177--178 (2015) Full Text: DOI
Aptekarev, A. I.; Denisov, S. A.; Tulyakov, D. N. V. A. Steklov’s problem of estimating the growth of orthogonal polynomials. (English. Russian original) Zbl 1342.33016 Proc. Steklov Inst. Math. 289, 72-95 (2015); translation from Tr. Mat. Inst. Steklova 289, 83-106 (2015). Reviewer: Valery V. Karachik (Chelyabinsk) MSC: 33C45 42C05 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., Proc. Steklov Inst. Math. 289, 72--95 (2015; Zbl 1342.33016); translation from Tr. Mat. Inst. Steklova 289, 83--106 (2015) Full Text: DOI
Aptekarev, A. I.; López Lagomasino, G.; Martínez-Finkelshtein, A. Strong asymptotics for the Pollaczek multiple orthogonal polynomials. (English. Russian original) Zbl 1337.33006 Dokl. Math. 92, No. 3, 709-713 (2015); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 465, No. 4, 393-397 (2015). Reviewer: Peter Massopust (München) MSC: 33C47 15B52 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., Dokl. Math. 92, No. 3, 709--713 (2015; Zbl 1337.33006); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 465, No. 4, 393--397 (2015) Full Text: DOI
Aptekarev, Alexander I.; Yattselev, Maxim L. Padé approximants for functions with branch points – strong asymptotics of Nuttall-Stahl polynomials. (English) Zbl 1339.41020 Acta Math. 215, No. 2, 217-280 (2015). Reviewer: Marcel G. de Bruin (Haarlem) MSC: 41A21 30B40 30C85 31A15 PDFBibTeX XMLCite \textit{A. I. Aptekarev} and \textit{M. L. Yattselev}, Acta Math. 215, No. 2, 217--280 (2015; Zbl 1339.41020) Full Text: DOI arXiv
Aptekarev, A. I.; Tulyakov, D. N. The saturation regime of Meixner polynomials and the discrete Bessel kernel. (English. Russian original) Zbl 1325.33006 Math. Notes 98, No. 1, 180-184 (2015); translation from Mat. Zametki 98, No. 1, 147-151 (2015). MSC: 33C45 47B37 PDFBibTeX XMLCite \textit{A. I. Aptekarev} and \textit{D. N. Tulyakov}, Math. Notes 98, No. 1, 180--184 (2015; Zbl 1325.33006); translation from Mat. Zametki 98, No. 1, 147--151 (2015) Full Text: DOI
Aptekarev, A. I.; Draux, A.; Kalyagin, V. A.; Tulyakov, D. N. Asymptotics of sharp constants of Markov-Bernstein inequalities in integral norm with Jacobi weight. (English) Zbl 1332.41011 Proc. Am. Math. Soc. 143, No. 9, 3847-3862 (2015). Reviewer: Vladimir V. Peller (East Lansing) MSC: 41A20 33C45 42C05 47B99 30B70 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., Proc. Am. Math. Soc. 143, No. 9, 3847--3862 (2015; Zbl 1332.41011) Full Text: DOI arXiv
Aptekarev, A. I.; Toulyakov, D. N.; Van Assche, W. Hyperelliptic uniformization of algebraic curves of the third order. (English) Zbl 1312.33022 J. Comput. Appl. Math. 284, 38-49 (2015). MSC: 33C45 41A21 42C05 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., J. Comput. Appl. Math. 284, 38--49 (2015; Zbl 1312.33022) Full Text: DOI arXiv
Aptekarev, A. I.; Derevyagin, M.; van Assche, W. On 2D discrete Schrödinger operators associated with multiple orthogonal polynomials. (English) Zbl 1393.39012 J. Phys. A, Math. Theor. 48, No. 6, Article ID 065201, 16 p. (2015). MSC: 39A70 33C50 47F05 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., J. Phys. A, Math. Theor. 48, No. 6, Article ID 065201, 16 p. (2015; Zbl 1393.39012) Full Text: DOI arXiv Link
Aptekarev, A.; Arvesú, J. Asymptotics for multiple Meixner polynomials. (English) Zbl 1331.33028 J. Math. Anal. Appl. 411, No. 2, 485-505 (2014). MSC: 33C47 42C05 PDFBibTeX XMLCite \textit{A. Aptekarev} and \textit{J. Arvesú}, J. Math. Anal. Appl. 411, No. 2, 485--505 (2014; Zbl 1331.33028) Full Text: DOI arXiv
Aptekarev, A. I.; Tulyakov, D. N. The leading term of the Plancherel-Rotach asymptotic formula for solutions of recurrence relations. (English. Russian original) Zbl 1317.39001 Sb. Math. 205, No. 12, 1696-1719 (2014); translation from Mat. Sb. 205, No. 12, 17-40 (2014). Reviewer: Raghib Abu-Saris (Edmonton) MSC: 39A06 39A22 PDFBibTeX XMLCite \textit{A. I. Aptekarev} and \textit{D. N. Tulyakov}, Sb. Math. 205, No. 12, 1696--1719 (2014; Zbl 1317.39001); translation from Mat. Sb. 205, No. 12, 17--40 (2014) Full Text: DOI
Aptekarev, A. I.; Dehesa, J. S.; Sánchez-Moreno, P.; Tulyakov, D. N. Asymptotics of \(L_p\)-norms of Hermite polynomials and Rényi entropy of Rydberg oscillator states. (English) Zbl 1318.94027 Arvesú, Jorge (ed.) et al., Recent advances in orthogonal polynomials, special functions, and their applications. 11th international symposium, Universidad Carlos III de Madrid, Leganés, Spain, August 29 – September 2, 2011. Proceedings. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-6896-6/pbk). Contemporary Mathematics 578, 19-29 (2012). MSC: 94A17 11B37 33C45 42C05 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., Contemp. Math. 578, 19--29 (2012; Zbl 1318.94027) Full Text: DOI arXiv
Aptekarev, A. I.; Tulyakov, D. N. Asymptotics of Meixner polynomials and Christoffel-Darboux kernels. (English. Russian original) Zbl 1271.33003 Trans. Mosc. Math. Soc. 2012, 67-106 (2012); translation from Tr. Mosk. Mat. O.-va 73, No. 1, 87-132 (2012). MSC: 33C45 60B10 PDFBibTeX XMLCite \textit{A. I. Aptekarev} and \textit{D. N. Tulyakov}, Trans. Mosc. Math. Soc. 2012, 67--106 (2012; Zbl 1271.33003); translation from Tr. Mosk. Mat. O.-va 73, No. 1, 87--132 (2012) Full Text: DOI
Aptekarev, A. I.; Lysov, V. G. [Bogolyubskii, A. I.] Asymptotic \(\gamma\)-forms generated by multiple orthogonal polynomials. (English. Russian original) Zbl 1317.33004 Proc. Steklov Inst. Math. 272, Suppl. 2, S168-S173 (2011); translation from Sovrem. Probl. Mat. 9, 55-62 (2007). Reviewer: Andrei A. Kapaev (St. Petersburg) MSC: 33C45 41A60 30E10 PDFBibTeX XMLCite \textit{A. I. Aptekarev} and \textit{V. G. Lysov}, Proc. Steklov Inst. Math. 272, S168--S173 (2011; Zbl 1317.33004); translation from Sovrem. Probl. Mat. 9, 55--62 (2007) Full Text: DOI
Aptekarev, A. I.; Tulyakov, D. N. Four-term recurrence relations for \(\gamma\)-forms. (English. Russian original) Zbl 1317.33008 Proc. Steklov Inst. Math. 272, Suppl. 2, S157-S161 (2011); translation from Sovrem. Probl. Mat. 9, 37-43 (2007). Reviewer: Andrei A. Kapaev (St. Petersburg) MSC: 33C47 33C45 11Y60 33F05 PDFBibTeX XMLCite \textit{A. I. Aptekarev} and \textit{D. N. Tulyakov}, Proc. Steklov Inst. Math. 272, S157--S161 (2011; Zbl 1317.33008); translation from Sovrem. Probl. Mat. 9, 37--43 (2007) Full Text: DOI
Aptekarev, A. I.; Kuijlaars, A. B. J. Hermite-Padé approximations and multiple orthogonal polynomial ensembles. (English. Russian original) Zbl 1243.41004 Russ. Math. Surv. 66, No. 6, 1133-1199 (2011); translation from Usp. Mat. Nauk 66, No. 6, 123-190 (2011). Reviewer: Marcel G. de Bruin (Haarlem) MSC: 41A21 30C15 31A15 42C05 60B20 60G17 60G55 PDFBibTeX XMLCite \textit{A. I. Aptekarev} and \textit{A. B. J. Kuijlaars}, Russ. Math. Surv. 66, No. 6, 1133--1199 (2011; Zbl 1243.41004); translation from Usp. Mat. Nauk 66, No. 6, 123--190 (2011) Full Text: DOI
Aptekarev, A. I.; Buslaev, V. I.; Martínez-Finkelshtein, A.; Suetin, S. P. Padé approximants, continued fractions, and orthogonal polynomials. (English. Russian original) Zbl 1242.41014 Russ. Math. Surv. 66, No. 6, 1049-1131 (2011); translation from Usp. Mat. Nauk 66, No. 6, 37-122 (2011). Reviewer: Yuri A. Farkov (Moscow) MSC: 41A21 30B70 42C05 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., Russ. Math. Surv. 66, No. 6, 1049--1131 (2011; Zbl 1242.41014); translation from Usp. Mat. Nauk 66, No. 6, 37--122 (2011) Full Text: DOI
Aptekarev, A. I.; Tulyakov, D. N. Asymptotic regimes in saturation zones for the C-D-kernels for an ensemble of Meixner orthogonal polynomials. (English. Russian original) Zbl 1218.30100 Russ. Math. Surv. 66, No. 1, 173-182 (2011); translation from Usp. Mat. Nauk. 66, No. 1, 181-182 (2011). MSC: 30E15 33C45 PDFBibTeX XMLCite \textit{A. I. Aptekarev} and \textit{D. N. Tulyakov}, Russ. Math. Surv. 66, No. 1, 173--182 (2011; Zbl 1218.30100); translation from Usp. Mat. Nauk. 66, No. 1, 181--182 (2011) Full Text: DOI
Aptekarev, A. I.; Lysov, V. G.; Tulyakov, D. N. Random matrices with external source and the asymptotic behaviour of multiple orthogonal polynomials. (English. Russian original) Zbl 1216.60008 Sb. Math. 202, No. 2, 155-206 (2011); translation from Mat. Sb. 202, No. 1, 3-56 (2011). MSC: 60B20 42C05 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., Sb. Math. 202, No. 2, 155--206 (2011; Zbl 1216.60008); translation from Mat. Sb. 202, No. 1, 3--56 (2011) Full Text: DOI
Aptekarev, A. I.; Lysov, V. G. Systems of Markov functions generated by graphs and the asymptotics of their Hermite-Padé approximants. (English. Russian original) Zbl 1188.42009 Sb. Math. 201, No. 2, 183-234 (2010); translation from Mat. Sb. 201, No. 2, 29-78 (2010). MSC: 42C05 41A21 30E25 PDFBibTeX XMLCite \textit{A. I. Aptekarev} and \textit{V. G. Lysov}, Sb. Math. 201, No. 2, 183--234 (2010; Zbl 1188.42009); translation from Mat. Sb. 201, No. 2, 29--78 (2010) Full Text: DOI
Aptekarev, A. I.; Dehesa, J. S.; Martínez-Finkelshtein, A.; Yáñez, R. J. Quantum expectation values of \(D\)-dimensional Rydberg hydrogenic states by use of Laguerre and Gegenbauer asymptotics. (English) Zbl 1188.81183 J. Phys. A, Math. Theor. 43, No. 14, Article ID 145204 (2010). MSC: 81V45 81Q35 33C45 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., J. Phys. A, Math. Theor. 43, No. 14, Article ID 145204 (2010; Zbl 1188.81183) Full Text: DOI
Aptekarev, A. I.; Dehesa, J. S.; Martinez-Finkelshtein, A. Asymptotics of orthogonal polynomial’s entropy. (English) Zbl 1183.94013 J. Comput. Appl. Math. 233, No. 6, 1355-1365 (2010). Reviewer: Pushpa N. Rathie (Brasilia) MSC: 94A17 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., J. Comput. Appl. Math. 233, No. 6, 1355--1365 (2010; Zbl 1183.94013) Full Text: DOI
Aptekarev, A. I.; Kalyagin, V. A.; Lysov, V. G.; Toulyakov, D. N. Equilibrium of vector potentials and uniformization of the algebraic curves of genus \(0\). (English) Zbl 1183.33012 J. Comput. Appl. Math. 233, No. 3, 602-616 (2009). Reviewer: Marcel G. de Bruin (Haarlem) MSC: 33C45 42C05 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., J. Comput. Appl. Math. 233, No. 3, 602--616 (2009; Zbl 1183.33012) Full Text: DOI
Aptekarev, A. I.; Dehesa, J. S.; Martínez-Finkelshtein, A.; Yáñez, R. Discrete entropies of orthogonal polynomials. (English) Zbl 1177.33018 Constr. Approx. 30, No. 1, 93-119 (2009). Reviewer: Alicia Cachafeiro López (Vigo) MSC: 33C45 41A58 42C05 94A17 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., Constr. Approx. 30, No. 1, 93--119 (2009; Zbl 1177.33018) Full Text: DOI arXiv
Aptekarev, A. I.; Geronimo, J. S.; Van Assche, W. Varying weights for orthogonal polynomials with monotonically varying recurrence coefficients. (English) Zbl 1143.42027 J. Approx. Theory 150, No. 2, 214-238 (2008). Reviewer: Stamatis Koumandos (Nicosia) MSC: 42C05 33C47 74Gxx 31-XX PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., J. Approx. Theory 150, No. 2, 214--238 (2008; Zbl 1143.42027) Full Text: DOI
Aptekarev, A.; Khabibullin, R. Asymptotic expansions for polynomials orthogonal with respect to a complex non-constant weight function. (English. Russian original) Zbl 1211.42025 Trans. Mosc. Math. Soc. 2007, 1-37 (2007); translation from Tr. Mosk. Mat. O.-va 68, 3-43 (2007). MSC: 42C05 30C10 41A60 PDFBibTeX XMLCite \textit{A. Aptekarev} and \textit{R. Khabibullin}, Trans. Mosc. Math. Soc. 2007, 1--37 (2007; Zbl 1211.42025); translation from Tr. Mosk. Mat. O.-va 68, 3--43 (2007) Full Text: DOI
Aptekarev, A.; Cachafeiro, A.; Marcellán, F. A scalar Riemann boundary value problem approach to orthogonal polynomials on the circle. (English) Zbl 1130.42025 J. Approximation Theory 141, No. 2, 174-181 (2006). Reviewer: Leonid Golinskii (Kharkov) MSC: 42C05 33C47 PDFBibTeX XMLCite \textit{A. Aptekarev} et al., J. Approx. Theory 141, No. 2, 174--181 (2006; Zbl 1130.42025) Full Text: DOI
Aptekarev, A. I.; Kalyagin, V.; López Lagomasino, G.; Rocha, I. A. On the limit behavior of recurrence coefficients for multiple orthogonal polynomials. (English) Zbl 1140.42011 J. Approx. Theory 139, No. 1-2, 346-370 (2006). Reviewer: Andrei Martínez Finkelshtein (Almeria) MSC: 42C05 47B36 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., J. Approx. Theory 139, No. 1--2, 346--370 (2006; Zbl 1140.42011) Full Text: DOI Link
Aptekarev, A. I.; López, G. L.; Rocha, I. A. Ratio asymptotics of Hermite-Padé polynomials for Nikishin systems. (English. Russian original) Zbl 1077.42015 Sb. Math. 196, No. 8, 1089-1107 (2005); translation from Mat. Sb. 196, No. 8, 3-20 (2005). MSC: 42C05 41A21 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., Sb. Math. 196, No. 8, 1089--1107 (2005; Zbl 1077.42015); translation from Mat. Sb. 196, No. 8, 3--20 (2005) Full Text: DOI
Aptekarev, A. I.; Van Assche, W. Scalar and matrix Riemann-Hilbert approach to the strong asymptotics of Padé approximants and complex orthogonal polynomials with varying weight. (English) Zbl 1061.30035 J. Approximation Theory 129, No. 2, 129-166 (2004). Reviewer: Arno Kuijlaars (Leuven) MSC: 30E25 30E10 30E15 41A21 41A60 42C05 PDFBibTeX XMLCite \textit{A. I. Aptekarev} and \textit{W. Van Assche}, J. Approx. Theory 129, No. 2, 129--166 (2004; Zbl 1061.30035) Full Text: DOI
Aptekarev, A. I.; Branquinho, A.; Van Assche, W. Multiple orthogonal polynomials for classical weights. (English) Zbl 1033.33002 Trans. Am. Math. Soc. 355, No. 10, 3887-3914 (2003). Reviewer: Juri M. Rappoport (Moskva) MSC: 33C45 42C05 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., Trans. Am. Math. Soc. 355, No. 10, 3887--3914 (2003; Zbl 1033.33002) Full Text: DOI
Aptekarev, A. I.; Branquinho, A. Padé approximants and complex high order Toda lattices. (English) Zbl 1031.42026 J. Comput. Appl. Math. 155, No. 2, 231-237 (2003). Reviewer: Andrei Martínez Finkelshtein (Almeria) MSC: 42C05 33C45 37K60 30B70 34B15 34M55 PDFBibTeX XMLCite \textit{A. I. Aptekarev} and \textit{A. Branquinho}, J. Comput. Appl. Math. 155, No. 2, 231--237 (2003; Zbl 1031.42026) Full Text: DOI
Aptekarev, Alexandre I.; Draux, André; Toulyakov, Dmitrii [Peherstorfer, F.] Discrete spectra of certain co-recursive Pollaczek polynomials and its applications. (English) Zbl 1061.33005 Comput. Methods Funct. Theory 2, No. 2, 519-537 (2002). MSC: 33C45 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., Comput. Methods Funct. Theory 2, No. 2, 519--537 (2002; Zbl 1061.33005) Full Text: DOI
Aptekarev, A. I.; López Lagomasino, G. T.; Marcellán, F. Orthogonal polynomials with respect to a differential operator. Existence and uniqueness. (English) Zbl 1029.42018 Rocky Mt. J. Math. 32, No. 2, 467-481 (2002). MSC: 42C05 33C45 33C47 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., Rocky Mt. J. Math. 32, No. 2, 467--481 (2002; Zbl 1029.42018) Full Text: DOI Link
Aptekarev, A. I. Sharp constants for rational approximations of analytic functions. (English. Russian original) Zbl 1041.30014 Sb. Math. 193, No. 1, 1-72 (2002); translation from Mat. Sb. 193, No. 1, 3-72 (2002). Reviewer: Jesus Illán González (Vigo) MSC: 30E10 41A20 31A15 41A44 PDFBibTeX XMLCite \textit{A. I. Aptekarev}, Sb. Math. 193, No. 1, 1--72 (2002; Zbl 1041.30014); translation from Mat. Sb. 193, No. 1, 3--72 (2002) Full Text: DOI
Aptekarev, A. I.; Van Assche, W. Asymptotics of discrete orthogonal polynomials and the continuum limit of the Toda lattice. (English) Zbl 1018.37042 J. Phys. A, Math. Gen. 34, No. 48, 10627-10637 (2001). Reviewer: A.Pickering (Salamanca) MSC: 37K10 42C05 33C45 PDFBibTeX XMLCite \textit{A. I. Aptekarev} and \textit{W. Van Assche}, J. Phys. A, Math. Gen. 34, No. 48, 10627--10637 (2001; Zbl 1018.37042) Full Text: DOI Link
Aptekarev, A.; Berriochoa, E.; Cachafeiro, A. On a characeterization of integrability for the reciprocal weight of orthogonal polynomials on the circle. (English) Zbl 0961.33010 Acta Appl. Math. 61, No. 1-3, 81-86 (2000). Reviewer: Josefina Alvarez (Las Cruces) MSC: 33C47 42C05 PDFBibTeX XMLCite \textit{A. Aptekarev} et al., Acta Appl. Math. 61, No. 1--3, 81--86 (2000; Zbl 0961.33010) Full Text: DOI
Aptekarev, A. I. Strong asymptotics of multiple orthogonal polynomials for Nikishin systems. (English. Russian original) Zbl 0957.42015 Sb. Math. 190, No. 5, 631-669 (1999); translation from Mat. Sb. 190, No. 5, 3-44 (1999). Reviewer: A.Lukashov (Saratov) MSC: 42C05 41A21 33C45 PDFBibTeX XMLCite \textit{A. I. Aptekarev}, Sb. Math. 190, No. 5, 631--669 (1999; Zbl 0957.42015); translation from Mat. Sb. 190, No. 5, 3--44 (1999) Full Text: DOI
Aptekarev, A.; Berriochoa, E.; Cachafeiro, A. Strong asymptotics for the continuous Sobolev orthogonal polynomials on the unit circle. (English) Zbl 0934.42017 J. Approximation Theory 100, No. 2, 381-391 (1999). Reviewer: Wiesław Pleśniak (Kraków) MSC: 42C05 30C45 PDFBibTeX XMLCite \textit{A. Aptekarev} et al., J. Approx. Theory 100, No. 2, 381--391 (1999; Zbl 0934.42017) Full Text: DOI
Aptekarev, A. I. Multiple orthogonal polynomials. (English) Zbl 0958.42015 J. Comput. Appl. Math. 99, No. 1-2, 423-447 (1998). Reviewer: Guillermo López Lagomasino (Leganes) MSC: 42C05 33C45 PDFBibTeX XMLCite \textit{A. I. Aptekarev}, J. Comput. Appl. Math. 99, No. 1--2, 423--447 (1998; Zbl 0958.42015) Full Text: DOI
Aptekarev, A. I.; Branquinho, A.; Marcellán, F. Toda-type differential equations for the recurrence coefficients of orthogonal polynomials and Freud transformation. (English) Zbl 0886.33007 J. Comput. Appl. Math. 78, No. 1, 139-160 (1997). Reviewer: Lothar Berg (Rostock) MSC: 33C45 47B15 15A60 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., J. Comput. Appl. Math. 78, No. 1, 139--160 (1997; Zbl 0886.33007) Full Text: DOI
Aptekarev, A. I.; Marcellán, F.; Rocha, I. A. Semiclassical multiple orthogonal polynomials and the properties of Jacobi-Bessel polynomials. (English) Zbl 0878.33004 J. Approximation Theory 90, No. 1, 117-146 (1997). Reviewer: F.Móricz (Szeged) MSC: 33C45 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., J. Approx. Theory 90, No. 1, 117--146 (1997; Zbl 0878.33004) Full Text: DOI
Aptekarev, A. I.; Buyarov, V. S.; Van Assche, W.; Dehesa, J. S. Asymptotics of entropy integrals for orthogonal polynomials. (English. Russian original) Zbl 0892.33005 Dokl. Math. 53, No. 1, 47-49 (1996); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 346, No. 4, 439-441 (1996). Reviewer: J.P.Singhal (Baroda) MSC: 33C45 94A17 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., Dokl. Math. 53, No. 1, 47--49 (1996; Zbl 0892.33005); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 346, No. 4, 439--441 (1996)
Aptekarev, A. I.; Buyarov, V. S.; Degeza, I. S. Asymptotic behavior of the \(L^ p\)-norms and the entropy for general orthogonal polynomials. (English. Russian original) Zbl 0862.46014 Russ. Acad. Sci., Sb., Math. 82, No. 2, 373-395 (1995); translation from Mat. Sb. 185, No. 8, 3-30 (1994). MSC: 46E30 28D20 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., Russ. Acad. Sci., Sb., Math. 82, No. 2, 3--30 (1994; Zbl 0862.46014); translation from Mat. Sb. 185, No. 8, 3--30 (1994) Full Text: DOI
Aptekarev, A. I.; Dehesa, J. S.; Yáñez, R. J. Spatial entropy of central potentials and strong asymptotics of orthogonal polynomials. (English) Zbl 0816.94010 J. Math. Phys. 35, No. 9, 4423-4428 (1994). MSC: 94A17 33C45 81Q05 PDFBibTeX XMLCite \textit{A. I. Aptekarev} et al., J. Math. Phys. 35, No. 9, 4423--4428 (1994; Zbl 0816.94010) Full Text: DOI
Aptekarev, A. I. Asymptotic behavior of orthogonal polynomials in the neighborhood of the ends of the orthogonality interval. (Russian) Zbl 0772.33003 Mat. Sb. 183, No. 5, 43-62 (1992). Reviewer: A.Lukashov (Saratov) MSC: 33C45 42C05 PDFBibTeX XMLCite \textit{A. I. Aptekarev}, Mat. Sb. 183, No. 5, 43--62 (1992; Zbl 0772.33003)
Aptekarev, A. I. Asymptotics of orthogonal polynomials in the neighborhood of the endpoints of the interval of orthogonality. (English. Russian original) Zbl 0782.33005 Russ. Acad. Sci., Sb., Math. 76, No. 1, 35-50 (1993); translation from Mat. Sb. 183, No. 5, 43-62 (1992). MSC: 33C45 42C05 PDFBibTeX XMLCite \textit{A. I. Aptekarev}, Russ. Acad. Sci., Sb., Math. 76, No. 1, 35--50 (1992; Zbl 0782.33005); translation from Mat. Sb. 183, No. 5, 43--62 (1992) Full Text: DOI
Aptekarev, A. I. Asymptotics of simultaneously orthogonal polynomials in the Angelesco case. (English. Russian original) Zbl 0744.42008 Math. USSR, Sb. 64, No. 1, 57-84 (1989); translation from Mat. Sb., Nov. Ser. 136(178), No. 1(5), 56-84 (1988). MSC: 42C05 41A60 33C45 PDFBibTeX XMLCite \textit{A. I. Aptekarev}, Math. USSR, Sb. 64, No. 1, 57--84 (1989; Zbl 0744.42008); translation from Mat. Sb., Nov. Ser. 136(178), No. 1(5), 56--84 (1988) Full Text: DOI
Aptekarev, A. I. Asymptotics of polynomials of simultaneous orthogonality in Angelesko’s case. (Russian) Zbl 0681.42015 Mat. Sb., N. Ser. 136(178), No. 1(5), 56-84 (1988). Reviewer: G.López Lagomasino MSC: 42C05 33C45 41A60 PDFBibTeX XMLCite \textit{A. I. Aptekarev}, Mat. Sb., Nov. Ser. 136(178), No. 1(5), 56--84 (1988; Zbl 0681.42015) Full Text: EuDML
Aptekarev, A. I. Asymptotic properties of polynomials orthogonal on a system of contours, and periodic motions of Toda lattices. (English. Russian original) Zbl 0608.42016 Math. USSR, Sb. 53, 233-260 (1986); translation from Mat. Sb., Nov. Ser. 125(167), No. 2, 231-258 (1984). Reviewer: A.G.Baskakov MSC: 42C05 30E15 PDFBibTeX XMLCite \textit{A. I. Aptekarev}, Math. USSR, Sb. 53, 233--260 (1986; Zbl 0608.42016); translation from Mat. Sb., Nov. Ser. 125(167), No. 2, 231--258 (1984) Full Text: DOI EuDML