메뉴 건너뛰기




Volumn 73, Issue 1, 2000, Pages 55-81

On Positive Definiteness of Some Functions

Author keywords

Positive definite, Schoenberg problems, Fourier transform, Bochner theorem, L vy theorem, Hausdorff Bernstein Widder theorem.

Indexed keywords


EID: 0037907102     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmva.1999.1864     Document Type: Article
Times cited : (57)

References (44)
  • 2
    • 52449145585 scopus 로고    scopus 로고
    • Fejer means for multivariate Fourier series
    • Berens H., Xu Y. Fejer means for multivariate Fourier series. Math. Zeitschrift. 221:1996;449-465.
    • (1996) Math. Zeitschrift , vol.221 , pp. 449-465
    • Berens, H.1    Xu, Y.2
  • 3
    • 21744438333 scopus 로고    scopus 로고
    • 1-summability of multiple Fourier integrals and positivity
    • 1-summability of multiple Fourier integrals and positivity. Math. Proc. Camb. Phil. Soc. 122:1997;149-172.
    • (1997) Math. Proc. Camb. Phil. Soc. , vol.122 , pp. 149-172
    • Berens, H.1    Xu, Y.2
  • 6
    • 0042886178 scopus 로고
    • Norm dependent positive definite functions on B-spaces
    • Christensen J. P. R., Ressel P. Norm dependent positive definite functions on B-spaces. Lecture Notes in Math. 990:1983;47-53.
    • (1983) Lecture Notes in Math. , vol.990 , pp. 47-53
    • Christensen, J.P.R.1    Ressel, P.2
  • 9
    • 0012040151 scopus 로고
    • Completely monotone functions and sequences
    • Feller W. Completely monotone functions and sequences. Trans. Amer. Math. Soc. 5:1939;662-774.
    • (1939) Trans. Amer. Math. Soc. , vol.5 , pp. 662-774
    • Feller, W.1
  • 11
    • 0001535351 scopus 로고    scopus 로고
    • On α-symmetric multivariate characteristic functions
    • Gneiting T. On α-symmetric multivariate characteristic functions. J. Multivariate Analysis. 64:1998;131-147.
    • (1998) J. Multivariate Analysis , vol.64 , pp. 131-147
    • Gneiting, T.1
  • 14
    • 0001756056 scopus 로고
    • On Abel-Poisson type and Riesz means
    • Golubov B. I. On Abel-Poisson type and Riesz means. Analysis Math. 7:1981;161-184.
    • (1981) Analysis Math. , vol.7 , pp. 161-184
    • Golubov, B.I.1
  • 15
    • 0003180011 scopus 로고
    • Schoenberg's problem on positive definite functions
    • Koldobsky A. Schoenberg's problem on positive definite functions. Algebra Anal. 3:1991;78-85.
    • (1991) Algebra Anal. , vol.3 , pp. 78-85
    • Koldobsky, A.1
  • 16
    • 0039223485 scopus 로고    scopus 로고
    • Positive definite functions, stable measures and isometries on Banach spaces
    • Koldobsky A. Positive definite functions, stable measures and isometries on Banach spaces. Lect. Notes in Pure and Appl. Math. 175:1996;275-290.
    • (1996) Lect. Notes in Pure and Appl. Math. , vol.175 , pp. 275-290
    • Koldobsky, A.1
  • 18
    • 0042385273 scopus 로고
    • Multidimensional versions and two problems of Schoenberg
    • Kuritsyn Y. Multidimensional versions and two problems of Schoenberg. Problems Stabil. Stochastic Models. 1989;72-79.
    • (1989) Problems Stabil. Stochastic Models , pp. 72-79
    • Kuritsyn, Y.1
  • 19
    • 0039436856 scopus 로고
    • On the Riesz means of a Fourier series
    • Kuttner B. On the Riesz means of a Fourier series. J. London Math. Soc. 19:1944;77-84.
    • (1944) J. London Math. Soc. , vol.19 , pp. 77-84
    • Kuttner, B.1
  • 20
    • 84963076018 scopus 로고
    • On positive Riesz and Abel typical means
    • Kuttner B. On positive Riesz and Abel typical means. Proc. London Math. Soc. 49:1947;328-352.
    • (1947) Proc. London Math. Soc. , vol.49 , pp. 328-352
    • Kuttner, B.1
  • 28
    • 0041883954 scopus 로고
    • Sufficient conditions for the characteristic functions of a two-dimensional isotropic distribution
    • Pasenchenko O. Yu. Sufficient conditions for the characteristic functions of a two-dimensional isotropic distribution. Teor. Imovirnost. ta Matem. Statyst. 53:1995;138-141.
    • (1995) Teor. Imovirnost. Ta Matem. Statyst. , vol.53 , pp. 138-141
    • Pasenchenko, O.Yu.1
  • 31
    • 0040793480 scopus 로고
    • Positive definite symmetric functions on finite dimensional spaces I. Applications of the Radon transform
    • Richards D. St. P. Positive definite symmetric functions on finite dimensional spaces I. Applications of the Radon transform. J. Multivariate Anal. 19:1986;280-298.
    • (1986) J. Multivariate Anal. , vol.19 , pp. 280-298
    • Richards, D.St.P.1
  • 32
    • 0040072717 scopus 로고
    • Positive definite symmetric functions on finite dimensional spaces II
    • Richards D. St. P. Positive definite symmetric functions on finite dimensional spaces II. Statistics and Probab. Letters. 3:1985;325-329.
    • (1985) Statistics and Probab. Letters , vol.3 , pp. 325-329
    • Richards, D.St.P.1
  • 33
    • 0001743201 scopus 로고
    • Metric spaces and completely monotone functions
    • Schoenberg I. J. Metric spaces and completely monotone functions. Ann. Math. 39:1938;811-841.
    • (1938) Ann. Math. , vol.39 , pp. 811-841
    • Schoenberg, I.J.1
  • 34
    • 84968492782 scopus 로고
    • Metric spaces and positive definite functions
    • Schoenberg I. J. Metric spaces and positive definite functions. Trans. Amer. Math. Soc. 44:1938;522-536.
    • (1938) Trans. Amer. Math. Soc. , vol.44 , pp. 522-536
    • Schoenberg, I.J.1
  • 36
    • 0041383102 scopus 로고
    • A criterion for a characteristic function and Polyá type criterion for radial functions of several variables
    • Trigub R. M. A criterion for a characteristic function and Polyá type criterion for radial functions of several variables. Theory Probab. Appl. 34:1989;738-742.
    • (1989) Theory Probab. Appl. , vol.34 , pp. 738-742
    • Trigub, R.M.1
  • 40
    • 84972529912 scopus 로고
    • Multiply monotone functions and their Laplace transforms
    • Williamson R. E. Multiply monotone functions and their Laplace transforms. Duke Math. J. 23:1956;189-207.
    • (1956) Duke Math. J. , vol.23 , pp. 189-207
    • Williamson, R.E.1
  • 42
    • 0038844166 scopus 로고
    • Positive definite functions depending on a norm
    • Zastavnyi V. P. Positive definite functions depending on a norm. Dokl. Russian Acad. Nauk. 325:1992;901-903.
    • (1992) Dokl. Russian Acad. Nauk , vol.325 , pp. 901-903
    • Zastavnyi, V.P.1
  • 43
    • 0039476867 scopus 로고
    • Positive definite functions depending on the norm
    • Zastavnyi V. P. Positive definite functions depending on the norm. Russian J. Math. Physics. 1:1993;511-522.
    • (1993) Russian J. Math. Physics , vol.1 , pp. 511-522
    • Zastavnyi, V.P.1
  • 44
    • 0042886177 scopus 로고
    • On some properties of one class of the radial positive definite functions
    • Kiev: Vyscha shkola 1995. p. 118-127
    • Zastavnyi V. P. On some properties of one class of the radial positive definite functions. Matematika Segodnya 94. 1995;Vyscha shkola 1995, Kiev. p. 118-127.
    • (1995) Matematika Segodnya 94
    • Zastavnyi, V.P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.