Linear differential equations with coefficients in weighted Bergman and Hardy spaces
نویسندگان
چکیده
منابع مشابه
Weighted Hardy-Sobolev Spaces and Complex Scaling of Differential Equations with Operator Coefficients
In this paper we study weighted Hardy-Sobolev spaces of vector valued functions analytic on double-napped cones of the complex plane. We introduce these spaces as a tool for complex scaling of linear ordinary differential equations with dilation analytic unbounded operator coefficients. As examples we consider boundary value problems in cylindrical domains and domains with quasicylindrical ends.
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For a range of Hardy and Bergman spaces X and sets of uniqueness K we show that for any functional φ ∈ X∗ there exists a sequence of measures (μn) supported on K converging weak* to φ. In particular, we consider H2 of the right half plane and obtain a Carleman–type formula for the continuous wavelet transform.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2008
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-07-04335-8