منابع مشابه
On growth of Lie algebras, generalized partitions, and analytic functions
In this paper we discuss some recent results on two diierent types of growth of Lie algebras, that lead to some combinatorial problems. First, we study the growth of nitely generated Lie algebras (sections 1{4). This problem leads to a study of generalized partitions. Recently the author has suggested a series of q-dimensions of algebras Dim q , q 2 N which includes, as rst terms, dimensions of...
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We define the algebra G̃(A) of Colombeau generalized functions on a subset A of the space of generalized points R̃d. If A is an open subset of R̃d, such generalized functions can be identified with pointwise maps from A into the ring of generalized numbers C̃. We study analyticity in G̃(A), where A is an open subset of C̃. In particular, if the domain is an open ball for the sharp norm on C̃, we chara...
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We compute the essential norm of a composition operator relatively to the class of Dunford-Pettis opertors or weakly compact operators, on some uniform algebras of analytic functions. Even in the frame of H∞ (resp. the disk algebra), this is new, as well for the polydisk algebras and the polyball algebras. This is a consequence of a general study of weighted composition operators.
متن کاملZygmund classes in algebras of generalized functions
We introduce an intrinsic notion of Zygmund regularity for Colombeau algebras of generalized functions. In case of embedded distributions belonging to some Zygmund-Hölder space this is shown to be consistent. The definition is motivated by the well-known use of the wavelet transform as a tool in studying Hölder-Zygmund regularity. It is based on a simple mollifier-wavelet interplay which transl...
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ژورنال
عنوان ژورنال: Banach Center Publications
سال: 1982
ISSN: 0137-6934,1730-6299
DOI: 10.4064/-8-1-467-470