اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAccentuate the negative
48
0
0.0
(
0
)
تأليف
P.S.Bullen
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
A survey of mean inequalities with real weights is given.
قيم البحث
اقرأ أيضاً
This paper is concerned with formally self-adjoint difference equations and their positive and negative deficiency indices. It is shown that the order of any formally self-adjoint difference equation is even, and some characterizations of formally se
lf-adjoint difference equations are established. Further, we show that the positive and negative deficiency indices are always equal, which implies the existence of the self-adjoint extensions of the minimal linear relations generated by the difference equations. This is an important and essential difference between formally self-adjoint difference equations and their corresponding differential equations in the spectral theory.
New explicit as well as manifestly symmetric three-term summationformulas are derived for the Clausenian hypergeometric series $_3F_2(1)$ with negative integral parameter differences. Our results generalize and naturally extend several similar relati
ons published, in recent years, by many authors. An appropriate and useful connection is established with the quite underestimated 1974 paper by P. W. Karlsson.
Multifractal analysis aims to characterize signals, functions, images or fields, via the fluctuations of their local regularity along time or space, hence capturing crucial features of their temporal/spatial dynamics. Multifractal analysis is becomin
g a standard tool in signal and image processing, and is nowadays widely used in numerous applications of different natures. Its common formulation relies on the measure of local regularity via the Holder exponent, by nature restricted to positive values, and thus to locally bounded functions or signals. It is here proposed to base the quantification of local regularity on $p$-exponents, a novel local regularity measure potentially taking negative values. First, the theoretical properties of $p$-exponents are studied in detail. Second, wavelet-based multiscale quantities, the $p$-leaders, are constructed and shown to permit accurate practical estimation of $p$-exponents. Exploiting the potential dependence with $p$, it is also shown how the collection of $p$-exponents enriches the classification of locally singular behaviors in functions, signals or images. The present contribution is complemented by a companion article developing the $p$-leader based multifractal formalism associated to $p$-exponents.
Let $p(cdot): mathbb R^nto(0,1]$ be a variable exponent function satisfying the globally $log$-Holder continuous condition and $L$ a non-negative self-adjoint operator on $L^2(mathbb R^n)$ whose heat kernels satisfying the Gaussian upper bound estima
tes. Let $H_L^{p(cdot)}(mathbb R^n)$ be the variable exponent Hardy space defined via the Lusin area function associated with the heat kernels ${e^{-t^2L}}_{tin (0,infty)}$. In this article, the authors first establish the atomic characterization of $H_L^{p(cdot)}(mathbb R^n)$; using this, the authors then obtain its non-tangential maximal function characterization which, when $p(cdot)$ is a constant in $(0,1]$, coincides with a recent result by Song and Yan [Adv. Math. 287 (2016), 463-484] and further induces the radial maximal function characterization of $H_L^{p(cdot)}(mathbb R^n)$ under an additional assumption that the heat kernels of $L$ have the Holder regularity.
In this paper the effect of the search for a primitive on the theory of integration is discussed.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
