Versions of well known function theoretic operator theory results of Szego and Widom are established for the Neil algebra. The Neil algebra is the subalgebra of the algebra of bounded analytic functions on the unit disc consisting of those functions whose derivative vanishes at the origin.
Let $mathcal{H}_0=V, mathcal{H}_1=B+V$ and $mathcal{H}_2=mathcal{L}+V$ be the operators on the Heisenberg group $mathbb{H}^n$, where $V$ is the operator of multiplication growing like $|g|^kappa, 0<kappa<1$, $B$ is a bounded linear operator and $math
cal{L}$ is the sublaplacian on $mathbb{H}^n$. In this paper we prove Szego limit theorem for the operators $mathcal{H}_0, mathcal{H}_1$ and $mathcal{H}_2$ on $L^2(mathbb{H}^n).$
In this paper we consider an asymptotic question in the theory of the Gaussian Unitary Ensemble of random matrices. In the bulk scaling limit, the probability that there are no eigenvalues in the interval (0,2s) is given by P_s=det(I-K_s), where K_s
is the trace-class operator with kernel K_s(x,y)={sin(x-y)}/{pi(x-y)} acting on L^2(0,2s). We are interested particularly in the behavior of P_s as s tends to infinity...
We establish an Ergodic Theorem for lower probabilities, a generalization of standard probabilities widely used in applications. As a by-product, we provide a version for lower probabilities of the Strong Law of Large Numbers.
We consider a class of generalized nonexpansive mappings introduced by Karapinar [5] and seen as a generalization of Suzuki (C)-condition. We prove some weak and strong convergence theorems for approximating fixed points of such mappings under suitab
le conditions in uniformly convex Banach spaces. Our results generalize those of Khan and Suzuki [4] to the case of this kind of mappings and, in turn, are related to a famous convergence theorem of Reich [2] on nonexpansive mappings.
We prove an uncertainty principle for certain eigenfunction expansions on $ L^2(mathbb{R}^+,w(r)dr) $ and use it to prove analogues of theorems of Chernoff and Ingham for Laplace-Beltrami operators on compact symmetric spaces, special Hermite operato
r on $ mathbb{C}^n $ and Hermite operator on $ mathbb{R}^n.$