Results 161 to 170 of about 4,067 (192)

Lacunary Poisson Functions and Axial Harmonic Polynomials

Journal of the London Mathematical Society, 1991
``Our purpose is to produce three sharp results on three apparently independent subjects in the theory of harmonic functions.'' Let \(h(x)\), \(x=(x_ 1,x_ 2,\dots,x_ m)\), be a harmonic polynomial of degree \(m\) in \(R^ N\), \(N\geq 2\), such that \(h(0)=1\), \(h>0\) in the unit ball \(r\leq 1\).
Armitage, D. H., Kuran, Ü.
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Lacunary entire functions

Mathematical Proceedings of the Cambridge Philosophical Society, 1993
AbstractIt has been observed that lacunary functions and random functions often have many properties in common (cf. [5]). The present paper has the object of showing that lacunary entire functions behave in many respects like random entire functions. Both have the property of being large except in very small neighbourhoods of their zeros and these have
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\sigma-ASYMPTOTICALLY LACUNARY STATISTICAL EQUIVALENT FUNCTIONS ON AMENABLE SEMIGROUPS

Far East Journal of Applied Mathematics, 2017
[Abstract Not Available]
Kişi, Ömer, Güler, Erhan
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LACUNARY SERIES AND INDEPENDENT FUNCTIONS

Russian Mathematical Surveys, 1966
CONTENTSIntroductionChapter I. Lacunary subsystems of general systems of functions § 1. Definitions and notation § 2. Convergence § 3. Integrability § 4. Absolute convergence § 5. The central limit theorem § 6. The law of the iterated logarithmChapter II. Lacunary subsystems of specific systems of functions § 1. The trigonometric system § 2.
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Weighted Lacunary Maximal Functions on Curves

Canadian Mathematical Bulletin, 1995
AbstractLet γ(t) = (t, t2,..., tn) + a be a curve in Rn, where n ≥ 2 and a ∊ Rn. We prove LP-Lq estimates for the weighted lacunary maximal function, related to this curve, defined byIf n = 2 or 3 our results are (nearly) sharp.
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Norms of lacunary polynomials in functional spaces

Mathematical Notes, 1992
Let \(\Lambda\) be the space of functions \(f\) of the form \(f(x)= a_ 0+ \sum^ \infty_{k=1} a_ k\cos(n_ k x+ \psi_ k)\), where \(a_ k\in\mathbb{R}\), \(n_ k\in\mathbb{R}\), \(\psi_ k\in\mathbb{R}\) and \(n_{k+1}/n_ k\geq \lambda>1\) for some \(\lambda\), \(k=1,2,\dots,\) \((a_ k)\in l_ 2\). It is stated that \(\Lambda\subset\text{BMO}\) and the norm \(
Belov, A. S., Rodin, V. A.
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Oxidative photoreactivity of mono-transition-metal functionalized lacunary Keggin anions

Dalton Transactions, 2015
The photooxidative activity of mono-transition-metal functionalized lacunary silicotungstate Keggin anions is reported together with preliminary mechanistic insight into the photoreactivity.
M, Dave, C, Streb
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Characterization of lacunary functions in weighted Bergman–Besov–Lipschitz spaces

Complex Variables and Elliptic Equations, 2011
We consider the weighted Bergman–Besov–Lipschitz space B ρ of analytic functions F in the unit disc 𝔻 = {z ∈ ℂ, |z| ≤ 1} for which and we show that a lacunary function belongs to B ρ if and only if the sequence a n satisfies , where I n are diadic intervals defined by I n  = {k ∈ ℕ : 2 n−1 ≤ k   0 is a function of n and ρ.
E. Kwessi, G. De Souza, A. Abebe, R. Aulaskari   +3 more
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Lacunary series in weighted spaces of analytic functions

Archiv der Mathematik, 2011
Following \textit{A. L. Shields} and \textit{D. L. Williams} [Trans. Am. Math. Soc. 162(1971), 287--302 (1972; Zbl 0227.46034)], a positive function \(\psi\) defined on \([1,\infty)\) is said to be normal if there exist positive constants \(\alpha\) and \(\beta\) such that \(\psi(t)/t^\alpha\) is non-decreasing and \(\psi(t)/t^\beta\) is non-increasing
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Müntz-Szasz Theorems and Lacunary Entire Functions

1978
This lecture discusses the case of non-completeness for the Muntz-Szasz theorem and Malliavin’s theorem. Various applications to entire functions with gaps are presented.
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