Results 21 to 30 of about 471,877 (274)
Convergence rates for oversmoothing Banach space regularization
ETNA - Electronic Transactions on Numerical Analysis, 2022 This paper studies Tikhonov regularization for finitely smoothing operators in Banach spaces when the penalization enforces too much smoothness in the sense that the penalty term is not finite at the true solution. In a Hilbert space setting, Natterer (1984) showed with the help of spectral theory that optimal rates can be achieved in this situation. ('
Miller, Philip, Hohage, Thorsten
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Regularity of fuzzy convergence spaces [PDF]
Open Mathematics, 2018 Abstract(Fuzzy) convergence spaces are extensions of (fuzzy) topological spaces. ⊤-convergence spaces are one of important fuzzy convergence spaces. In this paper, we present an extending dual Fischer diagonal condition, and making use of this we discuss a regularity of ⊤-convergence spaces.
Li Lingqiang, Jin Qiu, Yao Bingxue
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Lattice-Valued Convergence Spaces: Weaker Regularity and
Abstract and Applied Analysis, 2014 By using some lattice-valued Kowalsky’s dual diagonal conditions, some weaker regularities for Jäger’s generalized stratifiedL-convergence spaces and those for Boustique et al’s stratifiedL-convergence spaces are defined and studied. Here, the latticeLis a complete Heyting algebra.
Li, Lingqiang, Jin, Qiu
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Optimal Convergence Rates for Tikhonov Regularization in Besov Spaces [PDF]
SIAM Journal on Numerical Analysis, 2020 This paper deals with Tikhonov regularization for linear and nonlinear ill-posed operator equations with wavelet Besov norm penalties. We show order optimal rates of convergence for finitely smoothing operators and for the backwards heat equation for a range of Besov spaces using variational source conditions.
Weidling, Frederic +2 more
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The regularity series of a convergence space II [PDF]
Bulletin of the Australian Mathematical Society, 1976 This study is a continuation of an earlier paper on the regularity series of a convergence space. The notions of aR-Hausdorff series and theT3-modification of a convergence space are introduced, and their relationship with the regularity series is studied. The concept of a symmetric space is shown to be useful in studyingT3-compactifications.
Kent, Darrell C., Richardson, G. D.
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Numerical approximation of stochastic evolution equations: Convergence in scale of Hilbert spaces [PDF]
, 2018 The present paper is devoted to the numerical approximation of an abstract stochastic nonlinear evolution equation in a separable Hilbert space {$\mathrm{H}$}. Examples of equations which fall into our framework include the GOY and Sabra shell models and
Bessaih, Hakima +3 more
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A class of completely regular spaces
International Journal of Mathematics and Mathematical Sciences, 1984 In this paper we investigate topologies with ultrafilters having bases of open sets. It is shown that these topologies are completely regular. All results are obtained by using Richardson's compactification of convergence spaces.
Patrik E. Eklund
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The regularity series of a convergence space [PDF]
Bulletin of the Australian Mathematical Society, 1975 The regularity series, or brieflyR-series, of a convergence space is an ordinal sequence of spaces leading to the regular modification of the space. The behavior of this series is studied relative to such basic constructs as products, subspaces, and various quotient maps.
Richardson, G. D., Kent, Darrell C.
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Preconvergence compactness and P-closed spaces
International Journal of Mathematics and Mathematical Sciences, 1984 In this article the major result characterizes preconvergence compactness in terms of the preconvergence closedness of second projections. Applying this result to a topological space (X,T) yields similar characterizations for H-closed, nearly compact ...
Robert A. Herrmann
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Uniform topology on EQ-algebras
Open Mathematics, 2017 In this paper, we use filters of an EQ-algebra E to induce a uniform structure (E, 𝓚), and then the part 𝓚 induce a uniform topology 𝒯 in E. We prove that the pair (E, 𝒯) is a topological EQ-algebra, and some properties of (E, 𝒯) are investigated.
Yang Jiang, Long Xin Xiao, He Peng Fei
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