اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدHadamard gap series in growth spaces
168
0
0.0
(
0
)
تأليف
Kjersti Solberg Eikrem
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Let $h^infty_v$ be the class of harmonic functions in the unit disk which admit a two-sided radial majorant $v(r)$. We consider functions $v $ that fulfill a doubling condition. We characterize functions in $h^infty_v$ that are represented by Hadamard gap series in terms of their coefficients, and as a corollary we obtain a characterization of Hadamard gap series in Bloch-type spaces for weights with a doubling property. We show that if $uin h^infty_v$ is represented by a Hadamard gap series, then $u $ will grow slower than $v$ or oscillate along almost all radii. We use the law of the iterated logarithm for trigonometric series to find an upper bound on the growth of a weighted average of the function $u $, and we show that the estimate is sharp.
قيم البحث
اقرأ أيضاً
We prove that iterating projections onto convex subsets of Hadamard spaces can behave in a more complicated way than in Hilbert spaces, resolving a problem formulated by Miroslav Bav{c}ak.
The purpose of this erratum is to correct the proof of Theorem A.0.1 in the appendix to our article ``Hadamard spaces with isolated flats math.GR/0411232, which was jointly authored by Mohamad Hindawi, Hruska and Kleiner. In that appendix, many of th
e results of math.GR/0411232 about CAT(0) spaces with isolated flats are extended to a more general setting in which the isolated subspaces are not necessarily flats. However, one step of that extension does not follow from the argument we used the isolated flats setting. We provide a new proof that fills this gap. In addition, we give a more detailed account of several other parts of Theorem A.0.1, which were sketched in math.GR/0411232.
Many different types of fractional calculus have been defined, which may be categorised into broad classes according to their properties and behaviours. Two types that have been much studied in the literature are the Hadamard-type fractional calculus
and tempered fractional calculus. This paper establishes a connection between these two definitions, writing one in terms of the other by making use of the theory of fractional calculus with respect to functions. By extending this connection in a natural way, a generalisation is developed which unifies several existing fractional operators: Riemann--Liouville, Caputo, classical Hadamard, Hadamard-type, tempered, and all of these taken with respect to functions. The fundamental calculus of these generalised operators is established, including semigroup and reciprocal properties as well as application to some example functions. Function spaces are constructed in which the new operators are defined and bounded. Finally, some formulae are derived for fractional integration by parts with these operators.
We construct a Schwartz function $varphi$ such that for every exponentially small perturbation of integers $Lambda$, the set of translates ${varphi(t-lambda), lambdainLambda}$ spans the space $L^p(R)$, for every $p > 1$. This result remains true for
more general function spaces $X$, whose norm is weaker than $L^1$ (on bounded functions).
We formulate general principles of building hypergeometric type series from the Jacobi theta functions that generalize the plain and basic hypergeometric series. Single and multivariable elliptic hypergeometric series are considered in detail. A char
acterization theorem for a single variable totally elliptic hypergeometric series is proved.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
