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Lobachevskii Journal of Mathematics
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Ershov, Yu. L., Schwidefsky, M. V.
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Ershov, Yu. L., Schwidefsky, M. V.
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Journal of the London Mathematical Society, 1990
A criterion is proposed for naturality of a norm on a space of analytic functions defined on the unit disc D in the complex plane \({\mathbb{C}}\), a criterion which seems to be satisfied in the usual examples of function spaces. A semi-normed space (X,p) of analytic functions on D is called natural if its closed unit ball \(X_ 1=\{f\in X:p(f)\leq 1\}\)
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A criterion is proposed for naturality of a norm on a space of analytic functions defined on the unit disc D in the complex plane \({\mathbb{C}}\), a criterion which seems to be satisfied in the usual examples of function spaces. A semi-normed space (X,p) of analytic functions on D is called natural if its closed unit ball \(X_ 1=\{f\in X:p(f)\leq 1\}\)
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Connectivity of Function Spaces
Canadian Journal of Mathematics, 1971Given two spaces X and Y with Y either an AE (metrizable) or ANE (metrizable), little is known with regard to when the function space (Yx, τ), for some topology τ, is an AE (metrizable) or ANE (metrizable) except when very strong separation properties are imposed on X and Y (see [5, pp. 186-189]).
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On the Functions on Linear Spaces
Acta Applicandae Mathematicae, 2005Let \({\mathbf V}\) be a linear space of dimension \(n\) over the field \(\text{GF}(q)\), consisting of \(q= p^m\) elements, where \(p\) is prime, and \({\mathbf F}\) be a set of functions from \({\mathbf V}\) to \({\mathbf V}\). The derivative of the function \(f\) and characteristic \(\mu{\mathbf I}(f)\) is considered as a measure of nonlinearity of ...
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The Dirichlet Space and Related Function Spaces
2019The study of the classical Dirichlet space is one of the central topics on the intersection of the theory of holomorphic functions and functional analysis. It was introduced about100 years ago and continues to be an area of active current research. The theory is related to such important themes as multipliers, reproducing kernels, and Besov spaces ...
Nicola Arcozzi +3 more
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On k-Spaces and Function Spaces
Proceedings of the American Mathematical Society, 1966Bagley, R. W., Yang, J. S.
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On the space of distribution functions
1982We adopt a defintion of distribution function that, although not new, is not common in the literature on probability; we introduce a new metric on the space of distribution functions and show that this space is both complete and compact.
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