JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (9): 137-142.doi: 10.6040/j.issn.1671-9352.0.2024.056

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Differentiability of operator-valued functions on discrete-time Bernoulli noise functionals

TANG Yuling   

  1. School of Mathematics, Hexi University, Zhangye 734000, Gansu, China
  • Published:2025-09-10

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Abstract: Let M be a discrete-time normal martingale that has the chaotic representation property and S(M)⊂L2(M)⊂S*(M) a Gelfand triple associated with M. Let L(S(M),S*(M)) be the space of all continuous linear operators from S(M) to S*(M) and O be an open subset of Rd. The differential of operator-valued functions from O to L(S(M),S*(M)) is investigated. Mainly using the 2D-Fock transform as a tool, a differentiability characterization theorem is obtained for operator-valued functions from O to L(S(M),S*(M)).

Key words: martingale, 2D-Fock transform, convolution, differentiability

CLC Number: 

  • O177
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