A complete orthonormal system of divergence
Copyright policy )A complete orthonormal system of divergence
A complete orthonormal system of functions {Θ n } n=1 ∞ ,Θ n ∈L [0,1] ∞ defined on the closed interval [0,1] is constructed such that ∑n=1∞anΘn diverges almost everywhere for any {an}n=1∞∉l2. For the constructed system the following result is true: Any nontrivial series by the system {Θn}n=1∞ which converges in measure to zero diverges almost everywhere.
independent functions, Independent functions, complete orthonormal system, Complete orthonormal system, Representation of functions by series, representation of functions by series, divergence, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, Completeness of sets of functions in nontrigonometric harmonic analysis, divergence almost everywhere, Analysis, Divergence almost everywhere
independent functions, Independent functions, complete orthonormal system, Complete orthonormal system, Representation of functions by series, representation of functions by series, divergence, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, Completeness of sets of functions in nontrigonometric harmonic analysis, divergence almost everywhere, Analysis, Divergence almost everywhere
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).3 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!