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Integral operators mapping into the space of bounded analytic functions [PDF]
, 2016 We address the problem of studying the boundedness, compactness and weak compactness of the integral operators $T_g(f)(z)=\int_0^z f(\zeta)g'(\zeta)\,d\zeta$ acting from a Banach space $X$ into $H^\infty$.
Manuel D. Contreras +3 more
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Algebras of entire functions containing functions of unbounded type on a Banach space
Karpatsʹkì Matematičnì Publìkacìï, 2021 In this paper, we consider algebras of entire analytic functions which are bounded on a prescribed family of balls in a Banach space. We investigate the structures of such algebras and describe their spectra in terms of spectra of algebras of uniformly ...
A. Zagorodnyuk, A. Hihliuk
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Helmholtz decomposition and potential functions for n-dimensional analytic vector fields [PDF]
Journal of Mathematical Analysis and Applications, 2021 The Helmholtz decomposition splits a sufficiently smooth vector field into a gradient field and a divergence-free rotation field. Existing decomposition methods impose constraints on the behavior of vector fields at infinity and require solving ...
E. Glötzl, Oliver Richters
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Euler spaces of analytic functions [PDF]
Transactions of the American Mathematical Society, 1988 A formula due to Euler and Legendre is used to construct finite-difference counterparts to the Dirichlet space. The spaces have integral representations and characterizations in terms of area integrals. Their reproducing kernels are logarithms of the reproducing kernels of the Newton spaces, which are counterparts to the Hardy class.
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On approximation of homomorphisms of algebras of entire functions on Banach spaces
Karpatsʹkì Matematičnì Publìkacìï, 2019 It is known due to R. Aron, B. Cole and T. Gamelin that every complex homomorphism of the algebra of entire functions of bounded type on a Banach space $X$ can be approximated in some sense by a net of point valued homomorphism. In this paper we consider
H.M. Pryimak
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A note on approximation of continuous functions on normed spaces
Karpatsʹkì Matematičnì Publìkacìï, 2020 Let $X$ be a real separable normed space $X$ admitting a separating polynomial. We prove that each continuous function from a subset $A$ of $X$ to a real Banach space can be uniformly approximated by restrictions to $A$ of functions, which are analytic ...
M.A. Mytrofanov, A.V. Ravsky
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Karpatsʹkì Matematičnì Publìkacìï, 2021 The work is devoted to the study of Fréchet algebras of symmetric (invariant under the composition of every of components of its argument with any measure preserving bijection of the domain of components of the argument) analytic functions on Cartesian ...
T.V. Vasylyshyn
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Hilbert spaces of analytic functions with a contractive backward shift [PDF]
Journal of Functional Analysis, 2018 We consider Hilbert spaces of analytic functions in the disk with a normalized reproducing kernel and such that the backward shift f ( z ) ↦ f ( z ) − f ( 0 ) z is a contraction on the space.
A. Aleman, Bartosz Malman
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Some Hilbert spaces of analytic functions. II [PDF]
Journal of Mathematical Analysis and Applications, 1963 This paper continues the study of Hilbert spaces of analytic functions which are involved in the structural analysis of nonself-adjoint transformations in Hilbert space. The theory of nonself-adjoint transformations originates in the quantum mechanical problems of nuclear scattering theory.
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Pointwise multipliers between spaces of analytic functions
Quaestiones Mathematicae, 2023 A Banach space X of analytic function in D, the unit disc in C, is said to be admissible if it contains the polynomials and convergence in X implies uniform convergence in compact subsets of D.If X and Y are two admissible Banach spaces of analytic functions in D and g is a holomorphic function in D, g is said to be a multiplier from X to Y if g · f ...
Daniel Girela, Noel Merchán
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