Results 291 to 300 of about 1,404,374 (329)

Remarks on mean convergence

Mathematical Notes of the Academy of Sciences of the USSR, 1977
In this article a necessary and sufficient condition is established for the validity of the Cauchy criterion in the class of sequences of functions {fn} of the set ϕ(L) which are convergent with respect to the ϕ-distance.
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MEAN CONVERGENCE OF SOME POSITIVE OPERATORS

Acta Mathematica Scientia, 1995
Summary: \(L^p\) convergence with \(0 ...
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Pointwise convergence of spherical means

Mathematical Proceedings of the Cambridge Philosophical Society, 1995
For a function f ∈ Lp(ℝd) we define the spherical meanswhere dσ is the rotationally invariant measure on Sd−1, normalized such that σ(Sd−1) = 1. We consider the problem of pointwise convergence of the means , for any particular sequence tj → 0.
Seeger, Andreas, Wainger, Stephen, Wright, James   +2 more
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The Mean Convergence of Orthogonal Series

American Journal of Mathematics, 1950
( 1) f~~~~~~(x) Y. anOn (X), n=0 ' b where an f (x)'n (x) dE (x).
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Weak$ {}^*$ convergence of operator means

Izvestiya: Mathematics, 2011
For a linear operator with on a Banach space we discuss conditions for the convergence of ergodic operator nets corresponding to the adjoint operator of in the -topology of the space . The accumulation points of all possible nets of this kind form a compact convex set in , which is the kernel of the operator semigroup , where .
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Mean convergence of Fourier series

Ukrainian Mathematical Journal, 1989
The author improves the results of \textit{S. A. Telyakovskij} [Mat. Zametki 1, 91-98 (1967; Zbl 0202.063)] dealing with the convergence in the metric L of series \((1)\quad a_ 0/2+\sum a_ k \cos kx\) and \((2)\quad \sum a_ k \sin kx.\) It is proved that if one of the conditions \(\lim_{n\to \infty}a_ n \log n=0\) formulated in the cited paper is ...
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Convergence in Mean, in Distribution

1989
We begin this lesson by reviewing the convergences introduced in Lessons 7 and 8, Part II; then we define and illustrate two new types. All together we will have the following “modes” of convergence: pointwise convergence, convergence almost surely,convergence a.s.
Hung T. Nguyen, Gerald S. Rogers
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Uniform Convergence of Empirical Means

2003
In this chapter, we study the first of the learning problems introduced in Chapter 3, namely the uniform convergence of empirical means to their true values as the number of samples approaches infinity. Two versions of this problem are studied. In the first version, the probability measure generating the samples is assumed to be known and fixed. In the
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Mean square convergence

2022
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Nörlund Means and Almost Convergence

Journal of the London Mathematical Society, 1978
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