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Pointwise Convergence of Fourier Series

The Annals of Mathematics, 1973
In this paper, we present a new proof of a theorem of Carleson and Hunt: The Fourier series of an LP function on [0, 2J] converges almost everywhere (p > 1). (See [1], [51.) Our proof is very much in the spirit of the classical theorem of Kolmogoroff-Seliverstoff-Plessner [8].
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Pointwise and Uniformly Convergent Sets of Matrices

SIAM Journal on Matrix Analysis and Applications, 1999
Conditions for pointwise convergent and uniformly convergent sets of real \(n \times n\) matrices \(A_j\) are studied. The indexed set \(\mathcal{A}\) \(=\{A_j\}\) is pointwise convergent if for each \(x\in \mathbb{R}^n\) there is an index sequence \(\{p(x)_i\}^{\infty}_{i=1}\) such that \(\lim_{k \rightarrow \infty}((\prod^k_{i=1}A_{p(x)_i})x)=0\) and
Adam L. Cohen   +2 more
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Pointwise Convergence and Uniform Convergence of Wavelet Frame Series

Acta Mathematica Sinica, English Series, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
exaly   +3 more sources

A New Convergence Analysis of Finite Element Methods for Elliptic Distributed Optimal Control Problems with Pointwise State Constraints

SIAM Journal of Control and Optimization, 2017
We consider finite element methods for elliptic distributed optimal control problems with pointwise state constraints on two and three dimensional convex polyhedral domains formulated as fourth order variational inequalities. We develop a new convergence
S. Brenner, L. Sung
semanticscholar   +1 more source

Comparison with Pointwise Convergence

1993
In the previous chapter we saw that, in general, Γ-convergence and point-wise convergence are independent. In this chapter we illustrate the relationships between Γ-limits and pointwise limits and give some conditions under which Γ-convergence and pointwise convergence are equivalent.
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POINTWISE CONVERGENCE OF DOUBLE WALSH SERIES

Analysis, 1992
The author proves several Tauberian type theorems for Walsh series whose coefficients satisfy certain generalized bounded variation conditions. Combining these theorems with known summability results, the author proves convergence theorems for a large class of double Walsh-Fourier series. Here is a typical example of what this article contains.
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Note on Pointwise Convergence on the Choquet Boundary

Canadian Mathematical Bulletin, 1967
In [6] J. Rainwater obtained the following theorem.Theorem. Let N be a normed linear space, {xn} a bounded sequence of elements in N and X ∊ N. for each extreme point f of the unit ball of N✶, then {xn} converges weakly to x.Now let X be a compact Hausdorff space and H a linear subspace of C(X) (all real-valued continuous functions on X ) which ...
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Pointwise Convergence along non-tangential direction for the Schrödinger equation with Complex Time

Revista Matemática Complutense, 2020
Jiye Yuan, Tengfei Zhao, Jiqiang Zheng
semanticscholar   +1 more source

Examples of a pointwise convergence of semigroups

1995
Summary: This article is a continuation of the paper [Semigroup Forum 49, No. 3, 303-327 (1994; Zbl 0817.47047)]. It contains further examples of families of semigroups approximating semigroups strongly continuous only on a subspace of the original Banach space.
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