We generalize a theorem of Nanduri expressing the Hilbert function for Schubert varieties in minuscule homogeneous spaces in terms of the combinatorics of the corresponding Bruhat graph.
This note contributes to the study of large-scale geometry. Specifically, we introduce the concept of intrinsically quasi-isometric sections in metric spaces and investigate their properties. In particular, we examine their Ahlfors-David regularity at large scales. Building on Cheeger's theory, we define appropriate sets that enable the determination of convexity and establish whether these sections form a vector space over R or C. Furthermore, inspired by Cheeger's approach, we propose an equivalence relation for this class of sections. Throughout the paper, we employ fundamental mathematical tools.
We show that the Bessel capacities can be characterized in terms of maximal function. The boundedness of maximal function associated with Radon-Nikodym type Bessel capacities will also be addressed.
In this paper, we give the rate of convergence of the conjugate Fourier integral of functions of bounded variation over (-infinity, infinity). Further, we give the rate of convergence of No & uml;rlund means of the conjugate Fourier integral of f, where f is of bounded variation over every finite interval [a, b], -infinity < a < b < infinity. Also, in particular as corollary, we get the rate of convergence of (C, 1) means of the conjugate Fourier integral.
We consider a sequence {Zn}n is an element of Z of weakly independent and identically distributed cylindrical random variables in a Banach space U and a bounded linear operator A on U and show that under suitable conditions, for each n is an element of Z, the series P infinity k =0 Zn-k((A & lowast;)k(& centerdot;)) converges in 2, where 2 is a Banach space of cylindrical random variables to be defined and if we define Yn := P infinity k =0 Zn-k((A & lowast;)k(& centerdot;)), then the cylindrical process {Yn}n is an element of Z is the unique cylindrical weakly stationary solution of the cylindrical difference equation Xn= AXn-1 +Zn. We show that without additional conditions on the operator A and the cylindrical distribution of Z1, the cylindrical distribution of Yn is A-decomposable. Further, we prove that under mild conditions on the cylindrical distribution of Z1, Yn is induced by a U-valued random variable and finally we show that under certain conditions, the process {Xn} is a cylindrical Markov process.
