No Access

BEST CONSTANTS IN NORMS OF RETARDED WICK PRODUCTS

AUREL I. STAN

Department of Mathematics, The Ohio State University at Marion, 1465 Mount Vernon Avenue, Marion, OH 43302, USA

https://doi.org/10.1142/S0219025710004139Cited by:2 (Source: Crossref)

Abstract

We find the best constant c(m, n, r), such that the inequality:

holds for all polynomials f and g of degree at most m and n, respectively, where X is a normally distributed random vector, ⋄_r denotes the r-retarded Wick product and ‖⋅‖ the L²-norm.

Keywords:

AMSC: 60G15, 60H40, 32A36

References

S. Janson , Gaussian Hilbert Spaces , Cambridge Tracts in Mathematics 129 ( Cambridge Univ. Press , 1997 ) . Crossref, Google Scholar
H.-H. Kuo , Gaussian Measures in Banach Spaces , Lect. Notes Math. 4 ( Springer-Verlag , 1975 ) . Crossref, Google Scholar
H.-H. Kuo , White Noise Distribution Theory ( CRC Press , 1996 ) . Google Scholar
H.-H. Kuo, K. Saitô and A. Stan, Quantum Information IV, eds. T. Hida and K. Saitô (World Scientific, 2002) pp. 115–126. Link, Google Scholar
A. Lanconelli and A. I. Stan, J. Appl. Math. Stoch. Anal. (2008), DOI: 10.1155/2008/254897. Google Scholar
D. Nualart , The Malliavin Calculus and Related Topics ( Springer-Verlag , 1995 ) . Crossref, Google Scholar
D. Nualart and M. Zakai, Positive and Strongly Positive Wiener Functionals, Barcelona Seminar on Stochastic Analysis, Progr. Probab. 32 (Birkhäuser, 1991) pp. 132–146. Google Scholar
N. Obata , White Noise Calculus and Fock Space , Lect. Notes Math. 1577 ( Springer-Verlag , 1994 ) . Crossref, Google Scholar
A. I. Stan, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 9, 169 (2006), DOI: 10.1142/S0219025706002299. Link, Web of Science, Google Scholar
A. I. Stan, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 11, 377 (2008), DOI: 10.1142/S0219025708003178. Link, Web of Science, Google Scholar