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1.
Let {D(s), s ≥ 0} be a non-decreasing Lévy process. The first-hitting time process {E(t), t ≥ 0} (which is sometimes referred to as an inverse subordinator) defined by $E(t) = \inf \{s: D(s) > t \}$E(t) = \inf \{s: D(s) > t \} is a process which has arisen in many applications. Of particular interest is the mean first-hitting time
U(t)=\mathbbEE(t)U(t)=\mathbb{E}E(t). This function characterizes all finite-dimensional distributions of the process E. The function U can be calculated by inverting the Laplace transform of the function [(U)\tilde](l) = (lf(l))-1\widetilde{U}(\lambda) = (\lambda \phi(\lambda))^{-1}, where ϕ is the Lévy exponent of the subordinator D. In this paper, we give two methods for computing numerically the inverse of this Laplace transform. The first is based on
the Bromwich integral and the second is based on the Post-Widder inversion formula. The software written to support this work
is available from the authors and we illustrate its use at the end of the paper. 相似文献
2.
A Toeplitz operator TfT_\phi with symbol f\phi in
L¥(\mathbbD)L^{\infty}({\mathbb{D}}) on the Bergman space
A2(\mathbbD)A^{2}({\mathbb{D}}), where
\mathbbD\mathbb{D} denotes the open unit disc, is radial if f(z) = f(|z|)\phi(z) = \phi(|z|) a.e. on
\mathbbD\mathbb{D}. In this paper, we consider the numerical ranges of such operators. It is shown that all finite line segments, convex hulls
of analytic images of
\mathbbD\mathbb{D} and closed convex polygonal regions in the plane are the numerical ranges of radial Toeplitz operators. On the other hand,
Toeplitz operators TfT_\phi with f\phi harmonic on
\mathbbD\mathbb{D} and continuous on
[`(\mathbbD)]{\overline{\mathbb{D}}} and radial Toeplitz operators are convexoid, but certain compact quasinilpotent Toeplitz operators are not. 相似文献
3.
Let S{\mathcal{S}} be a set of homeomorphisms of an open interval such that the group generated by S{\mathcal{S}} is disjoint, i.e., the graphs of any two distinct functions in it do not intersect. We give necessary and sufficient conditions for the system of Abel equations
f(f(x))=f(x)+l(f), f ? S\phi(f(x))=\phi(x)+\lambda(f),\quad f \in \mathcal{S} 相似文献
4.
F. M. Al-Oboudi 《Complex Analysis and Operator Theory》2011,5(3):647-658
Let A denote the class of analytic functions f, in the open unit disk E = {z : |z| < 1}, normalized by f(0) = f′(0) − 1 = 0. In this paper, we introduce and study the class STn,al,m(h){ST^{n,\alpha}_{\lambda,m}(h)} of functions f ? A{f\in A}, with
\fracDn,al fm(z)z 1 0{\frac{D^{n,\alpha}_\lambda f_m(z)}{z}\neq 0}, satisfying
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