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For C a bounded, injective operator with dense image, we define a C-regularized spectral distribution. This produces a functional calculus, f → f(B), from C∞(ℝ) into the space of closed densely defined operators, such that f(B)C is bounded when f has compact support. As an analogue of Stone's...
Representations of a complex form of the Lie algebra of the Euclidean group of the plane are found. Bases for the corresponding Hilbert spaces are given in terms of Lommel polynomials and Bessel functions. An element of the Lie algebra is interpreted as a quantum random variable leading to the...
The aim of this paper is to give a wide introduction to approximation concepts in the theory of stochastic differential equations. The paper is principally concerned with Zong-Zakai approximations. Our aim is to fill a gap in the literature caused by the complete lack of monographs on such...
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