메뉴 건너뛰기




Volumn 11, Issue 4, 2001, Pages 377-396

A complex approach to strict positive definiteness on spheres

Author keywords

Disk polynomials; Jacobi polynomials; Spheres; Strict positive definiteness

Indexed keywords


EID: 0347084809     PISSN: 10652469     EISSN: None     Source Type: Journal    
DOI: 10.1080/10652460108819326     Document Type: Article
Times cited : (6)

References (18)
  • 2
    • 0007018967 scopus 로고
    • Zonal harmonic functions from two-dimensional analogs of Jacobi polynomials
    • J.N. Boyd and P.N. Raychowdhury, Zonal harmonic functions from two-dimensional analogs of Jacobi polynomials, Applicable Anal. 16 (1983), No. 3, 243-259.
    • (1983) Applicable Anal. , vol.16 , Issue.3 , pp. 243-259
    • Boyd, J.N.1    Raychowdhury, P.N.2
  • 3
    • 0011576630 scopus 로고
    • Approximation using positive definite functions, Approximation theory VIII, Vol. 1
    • (College Station, TX, 1995), , World Sci. Publishing, River Edge, NJ
    • E.W. Cheney, Approximation using positive definite functions, Approximation theory VIII, Vol. 1 (College Station, TX, 1995), Ser. Approx. Decompos., World Sci. Publishing, River Edge, NJ, 6 (1995), 145-168.
    • (1995) Ser. Approx. Decompos. , vol.6 , pp. 145-168
    • Cheney, E.W.1
  • 4
    • 0346015481 scopus 로고    scopus 로고
    • Interpolation on spheres by positive definite functions. Approximation theory
    • Dekker, New York
    • E.W. Cheney and X. Sun, Interpolation on spheres by positive definite functions. Approximation theory, Monogr. Textbooks Pure Appl. Math., Dekker, New York, 212 (1998), 141-155.
    • (1998) Monogr. Textbooks Pure Appl. Math. , vol.212 , pp. 141-155
    • Cheney, E.W.1    Sun, X.2
  • 5
    • 0010762464 scopus 로고
    • Positive definite kernels on the complex Hilbert sphere
    • J.P.R. Christensen and P. Ressel, Positive definite kernels on the complex Hilbert sphere, Math. Z., 180 (1982), No. 2, 193-201.
    • (1982) Math. Z. , vol.180 , Issue.2 , pp. 193-201
    • Christensen, J.P.R.1    Ressel, P.2
  • 6
    • 0346015483 scopus 로고
    • Summability of Fourier expansions in terms of disc polynomials. Functions, series, operators, Vol. I, II
    • (Budapest, 1980), North-Holland, Amsterdam, New York
    • B. Dreseler and R. Hrach, Summability of Fourier expansions in terms of disc polynomials. Functions, series, operators, Vol. I, II, Colloq. Math. Soc. János Bolyai (Budapest, 1980), North-Holland, Amsterdam, New York, 35 (1983), 375-384.
    • (1983) Colloq. Math. Soc. János Bolyai , vol.35 , pp. 375-384
    • Dreseler, B.1    Hrach, R.2
  • 7
    • 0000669521 scopus 로고    scopus 로고
    • Scattered data fitting on the sphere. Mathematical methods for curves and surfaces, II (Lillehammer, 1997)
    • Vanderbilt Univ. Press, Nashville, TN
    • G.E. Fasshauer and L.L. Schumaker, Scattered data fitting on the sphere. Mathematical methods for curves and surfaces, II (Lillehammer, 1997), Innov. Appl. Math., Vanderbilt Univ. Press, Nashville, TN, 1998, 117-166,
    • (1998) Innov. Appl. Math. , pp. 117-166
    • Fasshauer, G.E.1    Schumaker, L.L.2
  • 8
    • 0004151494 scopus 로고
    • Cambridge University Press, Cambridge, New York
    • R.A. Horn and C.R. Johnson, Matrix analysis, Cambridge University Press, Cambridge, New York, 1985.
    • (1985) Matrix Analysis
    • Horn, R.A.1    Johnson, C.R.2
  • 11
    • 0010967060 scopus 로고
    • The addition formula for Laguerre polynomials
    • T.H. Koornwinder, The addition formula for Laguerre polynomials, SIAM J. Math. Anal., 8 (1977), No. 3, 535-540.
    • (1977) SIAM J. Math. Anal. , vol.8 , Issue.3 , pp. 535-540
    • Koornwinder, T.H.1
  • 12
    • 0002095317 scopus 로고
    • Two-variable analogues of the classical orthogonal polynomials. Theory and application of special functions
    • Math. Res. Center, Univ. Wisconsin, Madison, Wis., Academic Press, New York
    • T.H. Koornwinder, Two-variable analogues of the classical orthogonal polynomials. Theory and application of special functions, Proc. Advanced Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis., Academic Press, New York, 35 (1975), 435-495.
    • (1975) Proc. Advanced Sem. , vol.35 , pp. 435-495
    • Koornwinder, T.H.1
  • 13
    • 85013579658 scopus 로고    scopus 로고
    • Strict positive definiteness on spheres
    • V.A. Menegatto, Strict positive definiteness on spheres, Analysis 19 (1999), No. 3, 217-233.
    • (1999) Analysis , vol.19 , Issue.3 , pp. 217-233
    • Menegatto, V.A.1
  • 15
    • 0003449868 scopus 로고
    • Springer-Verlag, New York, Berlin
    • n, Springer-Verlag, New York, Berlin, 1980.
    • (1980) n
    • Rudin, W.1
  • 16
    • 0345913167 scopus 로고
    • Special Junctions related to representations of the group SU(n), of class I with respect to SU(n - 1) (n ≥ 3)
    • in Russian
    • R.L. Shapiro, Special Junctions related to representations of the group SU(n), of class I with respect to SU(n - 1) (n ≥ 3), Izv. Vys. Uchebn. Zaved., Matematika, 71 (1968), No. 4, 97-107 (in Russian).
    • (1968) Izv. Vys. Uchebn. Zaved., Matematika , vol.71 , Issue.4 , pp. 97-107
    • Shapiro, R.L.1
  • 17
    • 0001878701 scopus 로고
    • Positive definite functions on spheres
    • I.J. Schoenberg, Positive definite functions on spheres, Duke Math. J., 9 (1942), 96-108.
    • (1942) Duke Math. J. , vol.9 , pp. 96-108
    • Schoenberg, I.J.1
  • 18
    • 0042595743 scopus 로고    scopus 로고
    • Strictly positive definite functions on the complex Hilbert sphere
    • X. Sun and V.A. Menegatto, Strictly positive definite functions on the complex Hilbert sphere, Adv. Comput. Math. 11 (1999), 105-119.
    • (1999) Adv. Comput. Math. , vol.11 , pp. 105-119
    • Sun, X.1    Menegatto, V.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.