A type of Volterra operator
نویسندگان
چکیده
منابع مشابه
A type of Volterra operator
For p ≥ 1, taking the p-th root of this sup yields a norm and with this norm H(D) is a Banach space. When p = 2, this is Hilbert space and identifying the Taylor coefficients of such an f with a sequence we obtain an isometry from H(D) onto the classical sequence space l. In addition, there is a natural identification of functions in H(D) with functions in a closed subspace of L(T) by way of th...
متن کاملMean Value Problems of Flett Type for a Volterra Operator
In this note we give a generalization of a mean value problem which can be viewed as a problem related to Volterra operators. This problem can be seen as a generalization of a result concerning the zeroes of a Volterra operator in the Banach space of continuous functions with null integral on a compact interval.
متن کاملThe Volterra Operator
0 |f(s)|ds ≤ |t| ≤ 1. Therefore the image of Bp is (uniformly) bounded. By Arzela-Ascoli, V : L p[0, 1]→ C[0, 1] is compact. The preceeding argument does not go through when V acts on L1[0, 1]. In this case equicontinuity fails, as is demonstrated by the following family {fn} ⊂ B1: fn(s) = n1[0,1/n](s). This suffices to preclude compactness of V ; in particular, V fn has no Cauchy subsequence. ...
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چکیده ندارد.
Local Operators and a Characterization of the Volterra Operator
We consider locally defined operators of the form D ◦K where D is the operator of differentiation and K maps the space of continuous functions into the space of n-times differentiable functions. As a corollary we obtain a characterization of the Volterra operator. Locally defined operators acting in the space of analytic functions are also discussed.
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ژورنال
عنوان ژورنال: Complex Analysis and its Synergies
سال: 2016
ISSN: 2197-120X
DOI: 10.1186/s40627-016-0007-9