메뉴 건너뛰기




Volumn 127, Issue 1-2, 2001, Pages 317-347

Some classical multiple orthogonal polynomials

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL GEOMETRY; COMPUTATIONAL METHODS; MATHEMATICAL OPERATORS; POLES AND ZEROS; THEOREM PROVING;

EID: 0035156173     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(00)00503-3     Document Type: Article
Times cited : (146)

References (63)
  • 4
    • 0032206942 scopus 로고    scopus 로고
    • Multiple orthogonal polynomials
    • Aptekarev A.I. Multiple orthogonal polynomials. J. Comput. Appl. Math. 99:1998;423-447.
    • (1998) J. Comput. Appl. Math. , vol.99 , pp. 423-447
    • Aptekarev, A.I.1
  • 6
    • 0034337982 scopus 로고    scopus 로고
    • Genetic sum representation for the moments of a system of Stieltjes functions and its application
    • to appear
    • A.I. Aptekarev, V. Kaliaguine (Kalyagin), J. Van Iseghem, Genetic sum representation for the moments of a system of Stieltjes functions and its application, Constr. Approx., to appear.
    • Constr. Approx.
    • Aptekarev, A.I.1    Kaliaguine, V.2    Van Iseghem, J.3
  • 7
    • 0031184852 scopus 로고    scopus 로고
    • Semiclassical multiple orthogonal polynomials and the properties of Jacobi-Bessel polynomials
    • Aptekarev A.I., Marcellán F., Rocha I.A. Semiclassical multiple orthogonal polynomials and the properties of Jacobi-Bessel polynomials. J. Approx. Theory. 90:1997;117-146.
    • (1997) J. Approx. Theory , vol.90 , pp. 117-146
    • Aptekarev, A.I.1    Marcellán, F.2    Rocha, I.A.3
  • 8
    • 21344488147 scopus 로고
    • On a class of Gauss-like quadrature rules
    • Borges C.F. On a class of Gauss-like quadrature rules. Numer. Math. 67:1994;271-288.
    • (1994) Numer. Math. , vol.67 , pp. 271-288
    • Borges, C.F.1
  • 10
    • 0040684094 scopus 로고
    • Some aspects of simultaneous rational approximation
    • Banach Center Publications 24, PWN-Polish Scientific Publishers, Warsaw
    • M.G. de Bruin, Some aspects of simultaneous rational approximation, in: Numerical Analysis and Mathematical Modeling, Banach Center Publications 24, PWN-Polish Scientific Publishers, Warsaw, 1990, pp. 51-84.
    • (1990) In: Numerical Analysis and Mathematical Modeling , pp. 51-84
    • De Bruin, M.G.1
  • 11
    • 0001664212 scopus 로고
    • Hermite-Padé approximation for Nikishin systems of analytic functions
    • J. Bustamante, G. López, Hermite-Padé approximation for Nikishin systems of analytic functions, Mat. Sb. 183 (1992) 117-138; translated in Math. USSR Sb. 77 (1994) 367-384.
    • (1992) Mat. Sb. , vol.183 , pp. 117-138
    • Bustamante, J.1    López, G.2
  • 12
    • 0040684097 scopus 로고
    • translated in
    • J. Bustamante, G. López, Hermite-Padé approximation for Nikishin systems of analytic functions, Mat. Sb. 183 (1992) 117-138; translated in Math. USSR Sb. 77 (1994) 367-384.
    • (1994) Math. USSR Sb. , vol.77 , pp. 367-384
  • 14
    • 0002987022 scopus 로고
    • Les Polynômes orthogonaux 'classiques' de dimension deux
    • Douak K., Maroni P. Les Polynômes orthogonaux 'classiques' de dimension deux. Analysis. 12:1992;71-107.
    • (1992) Analysis , vol.12 , pp. 71-107
    • Douak, K.1    Maroni, P.2
  • 15
    • 0009352932 scopus 로고
    • Une Caractérisation des polynômes d-orthogonaux 'classiques'
    • Douak K., Maroni P. Une Caractérisation des polynômes d-orthogonaux 'classiques'. J. Approx. Theory. 82:1995;177-204.
    • (1995) J. Approx. Theory , vol.82 , pp. 177-204
    • Douak, K.1    Maroni, P.2
  • 16
    • 0001332561 scopus 로고
    • Normality in Nikishin systems
    • Driver K., Stahl H. Normality in Nikishin systems. Indag. Math., N.S. 5(2):1994;161-187.
    • (1994) Indag. Math., N.S. , vol.5 , Issue.2 , pp. 161-187
    • Driver, K.1    Stahl, H.2
  • 17
    • 0001323471 scopus 로고
    • Simultaneous rational approximants to Nikishin systems, I, II
    • K. Driver, H. Stahl, Simultaneous rational approximants to Nikishin systems, I, II, Acta Sci. Math. (Szeged) 60 (1995) 245-263; 61 (1995) 261-284.
    • (1995) Acta Sci. Math. (Szeged) , vol.60 , pp. 245-263
    • Driver, K.1    Stahl, H.2
  • 18
    • 0000728926 scopus 로고
    • K. Driver, H. Stahl, Simultaneous rational approximants to Nikishin systems, I, II, Acta Sci. Math. (Szeged) 60 (1995) 245-263; 61 (1995) 261-284.
    • (1995) Acta Sci. Math. (Szeged) , vol.61 , pp. 261-284
  • 20
    • 0002512637 scopus 로고
    • On the convergence of simultaneous Padé approximants for systems of Markov type functions
    • A.A. Gonchar, E.A. Rakhmanov, On the convergence of simultaneous Padé approximants for systems of Markov type functions, Trudy Mat. Inst. Steklov 157 (1981) 31-48: translated in Proc. Steklov Math. Inst. 3 (1983) 31-50.
    • (1981) Trudy Mat. Inst. Steklov , vol.157 , pp. 31-48
    • Gonchar, A.A.1    Rakhmanov, E.A.2
  • 21
    • 0039498859 scopus 로고
    • translated in
    • A.A. Gonchar, E.A. Rakhmanov, On the convergence of simultaneous Padé approximants for systems of Markov type functions, Trudy Mat. Inst. Steklov 157 (1981) 31-48: translated in Proc. Steklov Math. Inst. 3 (1983) 31-50.
    • (1983) Proc. Steklov Math. Inst. , vol.3 , pp. 31-50
  • 22
    • 0002640389 scopus 로고    scopus 로고
    • Hermite-Padé approximants for systems of Markov-type functions
    • A.A. Gonchar, E.A. Rakhmanov, V.N. Sorokin, Hermite-Padé approximants for systems of Markov-type functions, Mat. Sb. 188 (1997) 33-58; translated in Russian Acad. Sci. Sb. Math. 188 (1997) 671-696.
    • (1997) Mat. Sb. , vol.188 , pp. 33-58
    • Gonchar, A.A.1    Rakhmanov, E.A.2    Sorokin, V.N.3
  • 23
    • 0031286532 scopus 로고    scopus 로고
    • translated in
    • A.A. Gonchar, E.A. Rakhmanov, V.N. Sorokin, Hermite-Padé approximants for systems of Markov-type functions, Mat. Sb. 188 (1997) 33-58; translated in Russian Acad. Sci. Sb. Math. 188 (1997) 671-696.
    • (1997) Russian Acad. Sci. Sb. Math. , vol.188 , pp. 671-696
  • 24
    • 0001393756 scopus 로고
    • On a class of polynomials defined by two orthogonality relations
    • in Russian
    • V.A. Kalyagin (Kaliaguine), On a class of polynomials defined by two orthogonality relations, Mat. Sb. 110 (1979) 609-627 (in Russian); translated in Math. USSR Sb. 38 (1981) 563-580.
    • (1979) Mat. Sb. , vol.110 , pp. 609-627
    • Kalyagin, V.A.1
  • 25
    • 0005204056 scopus 로고
    • translated in
    • V.A. Kalyagin (Kaliaguine), On a class of polynomials defined by two orthogonality relations, Mat. Sb. 110 (1979) 609-627 (in Russian); translated in Math. USSR Sb. 38 (1981) 563-580.
    • (1981) Math. USSR Sb. , vol.38 , pp. 563-580
  • 26
    • 0005507820 scopus 로고
    • Hermite-Padé approximants and spectral analysis of non-symmetric operators
    • V. Kalyagin (Kaliaguine), Hermite-Padé approximants and spectral analysis of non-symmetric operators, Mat. Sb. 185 (1994) 79-100; translated in Russian Acad. Sci. Sb. Math. 82 (1995) 199-216.
    • (1994) Mat. Sb. , vol.185 , pp. 79-100
    • Kalyagin, V.1
  • 27
    • 21944456516 scopus 로고
    • translated in
    • V. Kalyagin (Kaliaguine), Hermite-Padé approximants and spectral analysis of non-symmetric operators, Mat. Sb. 185 (1994) 79-100; translated in Russian Acad. Sci. Sb. Math. 82 (1995) 199-216.
    • (1995) Russian Acad. Sci. Sb. Math. , vol.82 , pp. 199-216
  • 28
    • 0347036648 scopus 로고
    • Characteristics of the spectra of higher order difference operators and the convergence of simultaneous rational approximations
    • V.A. Kalyagin (Kaliaguine), Characteristics of the spectra of higher order difference operators and the convergence of simultaneous rational approximations, Dokl. Akad. Nauk 340 (1) (1995) 15-17; translated in Dokl. Math. 51 (1) (1995) 11-13.
    • (1995) Dokl. Akad. Nauk , vol.340 , Issue.1 , pp. 15-17
    • Kalyagin, V.A.1
  • 29
    • 0039498857 scopus 로고
    • translated in
    • V.A. Kalyagin (Kaliaguine), Characteristics of the spectra of higher order difference operators and the convergence of simultaneous rational approximations, Dokl. Akad. Nauk 340 (1) (1995) 15-17; translated in Dokl. Math. 51 (1) (1995) 11-13.
    • (1995) Dokl. Math. , vol.51 , Issue.1 , pp. 11-13
  • 30
    • 0040684038 scopus 로고
    • On operators associated with Angelesco systems
    • Kaliaguine (Kalyagin) V.A. On operators associated with Angelesco systems. East J. Approx. 1:1995;157-170.
    • (1995) East J. Approx. , vol.1 , pp. 157-170
    • Kaliaguine, V.A.1
  • 31
    • 0012605411 scopus 로고
    • The operator moment problem, vector continued fractions and an explicit form of the Favard theorem for vector orthogonal polynomials
    • Kaliaguine (Kalyagin) V. The operator moment problem, vector continued fractions and an explicit form of the Favard theorem for vector orthogonal polynomials. J. Comput. Appl. Math. 65:1995;181-193.
    • (1995) J. Comput. Appl. Math. , vol.65 , pp. 181-193
    • Kaliaguine, V.1
  • 32
    • 0030101954 scopus 로고    scopus 로고
    • On a system of classical polynomials of simultaneous orthogonality
    • Kaliaguine (Kalyagin) V.A., Ronveaux A. On a system of classical polynomials of simultaneous orthogonality. J. Comput. Appl. Math. 67:1996;207-217.
    • (1996) J. Comput. Appl. Math. , vol.67 , pp. 207-217
    • Kaliaguine, V.A.1    Ronveaux, A.2
  • 34
    • 0001217669 scopus 로고
    • A uniform approach for Hermite-Padé and simultaneous Padé approximants and their matrix type generalization
    • Labahn G., Beckermann B. A uniform approach for Hermite-Padé and simultaneous Padé approximants and their matrix type generalization. Numer. Algorithms. 3:1992;45-54.
    • (1992) Numer. Algorithms , vol.3 , pp. 45-54
    • Labahn, G.1    Beckermann, B.2
  • 35
    • 0002728552 scopus 로고
    • Perfect systems
    • Mahler K. Perfect systems. Compositio Math. 19:1968;95-166.
    • (1968) Compositio Math. , vol.19 , pp. 95-166
    • Mahler, K.1
  • 36
    • 0001585426 scopus 로고
    • L'orthogonalité et les récurrences de polynômes d'ordre supérieur à deux
    • Maroni P. L'orthogonalité et les récurrences de polynômes d'ordre supérieur à deux. Ann. Fac. Sci. Toulouse. 10:1989;105-139.
    • (1989) Ann. Fac. Sci. Toulouse , vol.10 , pp. 105-139
    • Maroni, P.1
  • 39
    • 0003170213 scopus 로고
    • A system of Markov functions
    • E.M. Nikishin, A system of Markov functions, Vestnik Mosk. Univ., Ser. I (4) (1979) 60-63; translated in Moscow Univ. Math. Bull. 34 (1979) 63-66.
    • (1979) Vestnik Mosk. Univ., Ser. , vol.1 , Issue.4 , pp. 60-63
    • Nikishin, E.M.1
  • 40
    • 69649092193 scopus 로고
    • translated in
    • E.M. Nikishin, A system of Markov functions, Vestnik Mosk. Univ., Ser. I (4) (1979) 60-63; translated in Moscow Univ. Math. Bull. 34 (1979) 63-66.
    • (1979) Moscow Univ. Math. Bull. , vol.34 , pp. 63-66
  • 41
    • 0000816096 scopus 로고
    • On simultaneous Padé approximants
    • E.M. Nikishin, On simultaneous Padé approximants, Mat. Sb. 113 (115) (1980) 499-519; translated in Math. USSR Sb. 41 (1982) 409-425.
    • (1980) Mat. Sb. , vol.113 , Issue.115 , pp. 499-519
    • Nikishin, E.M.1
  • 42
    • 84956237856 scopus 로고
    • translated in
    • E.M. Nikishin, On simultaneous Padé approximants, Mat. Sb. 113 (115) (1980) 499-519; translated in Math. USSR Sb. 41 (1982) 409-425.
    • (1982) Math. USSR Sb. , vol.41 , pp. 409-425
  • 44
    • 0001350812 scopus 로고
    • Asymptotics of diagonal Hermite-Padé polynomials
    • Nuttall J. Asymptotics of diagonal Hermite-Padé polynomials. J. Approx. Theory. 42:1984;299-386.
    • (1984) J. Approx. Theory , vol.42 , pp. 299-386
    • Nuttall, J.1
  • 45
    • 0040684044 scopus 로고
    • The Jacobi-Perron algorithm and simultaneous approximation of functions
    • V.K. Parusnikov, The Jacobi-Perron algorithm and simultaneous approximation of functions. Mat. Sb. 114 (156) (1981) 322-333; translated in Math. USSR Sb. 42 (1982) 287-296.
    • (1981) Mat. Sb. , vol.114 , Issue.156 , pp. 322-333
    • Parusnikov, V.K.1
  • 46
    • 0000479215 scopus 로고
    • translated in
    • V.K. Parusnikov, The Jacobi-Perron algorithm and simultaneous approximation of functions. Mat. Sb. 114 (156) (1981) 322-333; translated in Math. USSR Sb. 42 (1982) 287-296.
    • (1982) Math. USSR Sb. , vol.42 , pp. 287-296
  • 47
    • 0001802525 scopus 로고
    • On simultaneous approximations for a collection of Markov functions
    • in Russian
    • L.R. Piñeiro, On simultaneous approximations for a collection of Markov functions, Vestnik Mosk. Univ., Ser. I (2) (1987) 67-70 (in Russian); translated in Moscow Univ. Math. Bull. 42 (2) (1987) 52-55.
    • (1987) Vestnik Mosk. Univ., Ser. , vol.1 , Issue.2 , pp. 67-70
    • Piñeiro, L.R.1
  • 48
    • 0040090568 scopus 로고
    • translated in
    • L.R. Piñeiro, On simultaneous approximations for a collection of Markov functions, Vestnik Mosk. Univ., Ser. I (2) (1987) 67-70 (in Russian); translated in Moscow Univ. Math. Bull. 42 (2) (1987) 52-55.
    • (1987) Moscow Univ. Math. Bull. , vol.42 , Issue.2 , pp. 52-55
  • 49
    • 0010797233 scopus 로고
    • Simultaneous Padé approximants for finite and infinite intervals
    • V.N. Sorokin, Simultaneous Padé approximants for finite and infinite intervals, Izv. Vyssh. Uchebn. Zaved., Mat. (8) (1984) (267) 45-52; translated in J. Soviet Math. 28 (8) (1984) 56-64.
    • (1984) Izv. Vyssh. Uchebn. Zaved., Mat. (8) , Issue.267 , pp. 45-52
    • Sorokin, V.N.1
  • 50
    • 0039498855 scopus 로고
    • translated in
    • V.N. Sorokin, Simultaneous Padé approximants for finite and infinite intervals, Izv. Vyssh. Uchebn. Zaved., Mat. (8) (1984) (267) 45-52; translated in J. Soviet Math. 28 (8) (1984) 56-64.
    • (1984) J. Soviet Math. , vol.28 , Issue.8 , pp. 56-64
  • 51
    • 0010863127 scopus 로고
    • A generalization of classical orthogonal polynomials and the convergence of simultaneous Padé approximants
    • V.N. Sorokin, A generalization of classical orthogonal polynomials and the convergence of simultaneous Padé approximants, Trudy Sem. Im. I. G. Petrovsk. 11 (1986) 125-165; translated in J. Soviet Math. 45 (1989) 1461-1499.
    • (1986) Trudy Sem. Im. I. G. Petrovsk. , vol.11 , pp. 125-165
    • Sorokin, V.N.1
  • 52
    • 0038906210 scopus 로고
    • translated in
    • V.N. Sorokin, A generalization of classical orthogonal polynomials and the convergence of simultaneous Padé approximants, Trudy Sem. Im. I. G. Petrovsk. 11 (1986) 125-165; translated in J. Soviet Math. 45 (1989) 1461-1499.
    • (1989) J. Soviet Math. , vol.45 , pp. 1461-1499
  • 53
    • 0038906151 scopus 로고
    • A generalization of Laguerre polynomials and convergence of simultaneous Padé approximants
    • V.N. Sorokin, A generalization of Laguerre polynomials and convergence of simultaneous Padé approximants, Uspekhi Mat. Nauk 41 (1986) 207-208; translated in Russian Math. Surveys 41 (1986) 245-246.
    • (1986) Uspekhi Mat. Nauk , vol.41 , pp. 207-208
    • Sorokin, V.N.1
  • 54
    • 0038906149 scopus 로고
    • translated in
    • V.N. Sorokin, A generalization of Laguerre polynomials and convergence of simultaneous Padé approximants, Uspekhi Mat. Nauk 41 (1986) 207-208; translated in Russian Math. Surveys 41 (1986) 245-246.
    • (1986) Russian Math. Surveys , vol.41 , pp. 245-246
  • 55
    • 0038906207 scopus 로고
    • Simultaneous Padé approximation for functions of Stieltjes type
    • V.N. Sorokin, Simultaneous Padé approximation for functions of Stieltjes type, Siber. Mat. Zh. 31 (5) (1990) 128-137; translated in Siber. Math. J. 31(5) (1990) 809-817.
    • (1990) Siber. Mat. Zh. , vol.31 , Issue.5 , pp. 128-137
    • Sorokin, V.N.1
  • 56
    • 0039498854 scopus 로고
    • translated in
    • V.N. Sorokin, Simultaneous Padé approximation for functions of Stieltjes type, Siber. Mat. Zh. 31 (5) (1990) 128-137; translated in Siber. Math. J. 31(5) (1990) 809-817.
    • (1990) Siber. Math. J. , vol.31 , Issue.5 , pp. 809-817
  • 57
    • 0031184846 scopus 로고    scopus 로고
    • Algebraic aspects of matrix orthogonality for vector polynomials
    • Sorokin V.N., Van Iseghem J. Algebraic aspects of matrix orthogonality for vector polynomials. J. Approx. Theory. 90:1997;97-116.
    • (1997) J. Approx. Theory , vol.90 , pp. 97-116
    • Sorokin, V.N.1    Van Iseghem, J.2
  • 61
    • 0003751806 scopus 로고    scopus 로고
    • Non-symmetric linear difference equations for multiple orthogonal polynomials
    • W. Van Assche, Non-symmetric linear difference equations for multiple orthogonal polynomials, CRM Proceedings and Lecture Notes, Vol. 25, 2000, pp. 391-405.
    • (2000) CRM Proceedings and Lecture Notes , vol.25 , pp. 391-405
    • Van Assche, W.1
  • 62
    • 0001255919 scopus 로고    scopus 로고
    • Multiple orthogonal polynomials associated with Macdonald functions
    • W. Van Assche, S.B. Yakubovich, Multiple orthogonal polynomials associated with Macdonald functions, Integral Transforms Special Functions, 9 (2000) 229-244.
    • Integral Transforms Special Functions , vol.9 , Issue.2000 , pp. 229-244
    • Van Assche, W.1    Yakubovich, S.B.2
  • 63
    • 0023378740 scopus 로고
    • Vector orthogonal relations, vector QD-algorithm
    • Van Iseghem J. Vector orthogonal relations, vector QD-algorithm. J. Comput. Appl. Math. 19:1987;141-150.
    • (1987) J. Comput. Appl. Math. , vol.19 , pp. 141-150
    • Van Iseghem, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.