ﻻ يوجد ملخص باللغة العربية
The classical Szeg{o}--Kolmogorov Prediction Theorem gives necessary and sufficient condition on a weight $w$ on the unite cirlce $T$ so that the exponentials with positive integer frequences span the weighted space $L^2(T,w)$. We consider the problem how many of these exponentials can be removed while still keeping the completeness property.
We present a characterization of sets for which Cartwrights theorem holds true. The connection is discussed between these sets and sampling sets for entire functions of exponential type.
In this paper, we prove a $Tb$ theorem on product spaces $Bbb R^ntimes Bbb R^m$, where $b(x_1,x_2)=b_1(x_1)b_2(x_2)$, $b_1$ and $b_2$ are para-accretive functions on $Bbb R^n$ and $Bbb R^m$, respectively.
We generalize the Kolmogorov continuity theorem and prove the continuity of a class of stochastic fields with the parameter. As an application, we derive the continuity of solutions for nonlocal stochastic parabolic equations driven by non-Gaussian L{e}vy noises.
We characterize even measures $mu=wdx+mu_s$ on the real line with finite entropy integral $int_{R} frac{log w(t)}{1+t^2}dt>-infty$ in terms of $2times 2$ Hamiltonian generated by $mu$ in the sense of inverse spectral theory. As a corollary, we obtain