Results 221 to 230 of about 70,649 (267)

OnA-Compact Operators, Generalized Entropy Numbers and Entropy Ideals

Mathematische Nachrichten, 1984
Using the notion of precompact subset in a Banach space, the authors introduce what are called A-compact sets referring to a given operator ideal A. Based upon this concept, A-compact operators are defined between Banach spaces. It is established that both A compact sets and A compact operators admit similar characterizations as precompact sets and ...
Carl, Bernd, Stephani, Irmtraud
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Entropy Numbers and Approximation Numbers in Function Spaces, II

Proceedings of the London Mathematical Society, 1989
This paper continues the study of entropy and approximation numbers related to compact embeddings between scales of Besov type function spaces \(B^ s_{p,q}\). In a previous paper [Proc. London Math Soc., III. Ser. 58, No. 1, 137-152 (1989; Zbl 0629.46034)], the authors obtained estimates from above for the entropy numbers \(e_ k\) and approximation ...
Edmunds, D. E, Triebel, H.
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Entropy numbers and interpolation

Mathematische Annalen, 2010
This paper settles a long-standing question by showing that in certain circumstances the entropy numbers of a map do not behave well under real interpolation, that is, that an inequality of the form \[ e_{m+n-1}(T: (X_0,X_1)_{\theta,q} \to (Y_0,Y_1)_{\theta,q}) \leq C \, e_m(T:X_0 \to Y_0)^{1-\theta} e_n(T:X_1 \to Y_1)^\theta \] is not possible in ...
Edmunds, DE, Netrusov, Y
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Entropy Numbers of Some Ergodic Averages

Theory of Probability & Its Applications, 2000
If \(X\) is a seminormed linear space and \(U\) a bounded linear operator on \(X\), we may consider the moving averages \(A_n= n^{-1} \sum^{n-1}_{j=0} U^j\), \(n= 1,2,\dots\). Given \(x\in X\), does a subsequence \(S\) of the sequence \(\{A_n(x)\}^\infty_{n=1}\) converge or cluster in some sense? The main thrust of this paper, building upon a result of
Gamet, C., Weber, M.
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Uniform Entropy Numbers

1996
In Section 2.5.1 the empirical process was shown to converge weakly for indexing sets F satisfying a uniform entropy condition. In particular, if $$ s\mathop u\limits_Q p\log N\left( {\varepsilon \parallel F{\parallel _{Q,2}},F,\mathop L\nolimits_2 \left( Q \right)} \right) \leqslant K{\left( {\frac{1}{\varepsilon }} \right)^{2 - \delta ...
Aad W. van der Vaart, Jon A. Wellner
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Gaussian Approximation Numbers and Metric Entropy

Journal of Mathematical Sciences, 2019
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Kühn, T., Linde, W.
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Entropy Numbers of Certain Summation Operators

gmj, 2001
Abstract Given nonnegative real sequences and we study the generated summation operator regarded as a mapping from ℓ p (ℤ) to ℓ q (ℤ).
Creutzig, J., Linde, W.
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The entropy source of pseudo random number generators: from low entropy to high entropy

2019 IEEE International Conference on Intelligence and Security Informatics (ISI), 2019
The pseudo random number generators (PRNG) is one type of deterministic functions. The information entropy of the output sequences depends on the entropy of the input seeds. The output sequences can be predicted if attackers could know or control the input seeds of PRNGs.
Jizhi Wang, Jingshan Pan, Xueli Wu
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Entropy numbers and interpolation

Mathematische Nachrichten, 1982
From the author's introduction. It is the purpose of this note to answer a query put forward by \textit{H. Triebel} in [Interpolation theory, function spaces, differential operators (1978; Zbl 0387.46032), p. 118], regarding interpolation properties of a certain class of operator ideals, the so-called entropy ideals.
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Some estimates on entropy numbers

Israel Journal of Mathematics, 1993
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Junge, Marius, Defant, Martin
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