Positive definite functions and dual pairs of locally convex spaces

• Autorzy: Alpay D. , Gabriyelyan S.

Identyfikatory

DOI

10.7494/OpMath.2018.38.4.463

• Języki publikacji: EN

Abstrakty

EN

Using pairs of locally convex topological vector spaces in duality and topologies defined by directed families of sets bounded with respect to the duality, we prove general factorization theorems and general dilation theorems for operator-valued positive definite functions.

Słowa kluczowe

EN

positive definite function locally convex space; dual pair; factorization property; dilation theory

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2018
• Tom: Vol. 38, no. 4
• Strony: 463--482
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Alpay D.

• Chapman University One University Drive Orange, California 92866, USA

autor

Gabriyelyan S.

• Department of Mathematics Ben Gurion University of the Negev P.O.B. 653, Be'er Sheva 84105, Israel

Bibliografia

• [1] J. Górniak, Locally convex spaces with factorization property, Colloq. Math. 48 (1984) 1, 69-79.
• [2] J. Górniak, A. Weron, Aronszajn-Kolrnogorov type theorems for positive definite kernels in locally convex spaces, Studia Math. 69 (1980/81) 3, 235-246.
• [3] M.A. Lifshits, Gaussian Random Functions, Kluwer Academic Publishers, 1995.
• [4] A. Makagon, Remark on the Extrapolation of Banach Space Valued Stationary Processes, Probability Theory on Vector Spaces, II (Proc. Second Internat. Conf., Blazejewko, 1979), Lecture Notes in Math., vol. 828, Springer, Berlin, 1980, 196-207.
• [5] A. Makagon, H. Salehi, Notes on Infinite-Dimensional Stationary Sequences, Probability theory on vector spaces, IV (Łańcut, 1987), Lecture Notes in Math., vol. 1391, Springer, Berlin, 1989, 200-238.
• [6] P. Masani, Dilations as propagators of Hilbertian varieties, SIAM J. Math. Anal. 9 (1978), 414-456.
• [7] L. Narici, E. Beckenstein, Topological Vector Spaces, second ed., Pure and Applied Mathematics (Boca Raton), vol. 296, CRC Press, Boca Raton, FL, 2011.
• [8] H. Niemi, A. Weron, Dilation theorems for positive definite operator kernels having majorants, J. Funct. Anal. 40 (1981) 1, 54-65.
• [9] G. Pedrick, Theory of reproducing kernels for Hilbert spaces of vector-valued functions, Univ. ol Kansas Tech. Rep. 19, Lawrence, 1957.
• [10] N.N. Vakhania, Probability Distributions on Linear Spaces, North-Holland Publishing Co., New York, 1981, Translated from the Russian by I.I. Kotlarski, North-Holland Series in Probability and Applied Mathematics.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).