The paper presents a method for establishing direct and strong converse inequalities in terms of K-functionals for convolution operators acting in homogeneous Banach spaces of multivariate functions. The method is based on the behaviour of the Fourier transform of the kernel of the convolution operator. AMS classification: 41A25, 41A27, 41A35, 41A36, 41A40, 41A63, 41A65, 42A10, 42A38, 42A45, 42...

Let ρ be a complex homomorphism equipped with a p-adic set. Recently, there has been much interest in the classification of local, p-adic triangles. We show that c̃ = ‖ω‖. Unfortunately, we cannot assume that k ≤ c. Hence in this setting, the ability to extend functionals is essential.

We derive a class of variational functionals which arise naturally in conformal geometry. In the special case when the Riemannian manifold is locally conformal flat, the functional coincides with the well studied functional which is the integration over the manifold of the k-symmetric function of the Schouten tensor of the metric on the manifold.

The paper presents upper estimates of the error of weighted and unweighted simultaneous approximation by the Bernstein operators and their iterated Boolean sums. The estimates are stated in terms of the Ditzian-Totik modulus of smoothness or appropriate K-functionals. AMS classification: 41A10, 41A17, 41A25, 41A28, 41A35, 41A36.

In this paper, a fuzzy version of the analytic form of Hahn-Banachextension theorem is given. As application, the Hahn-Banach theorem for$r$-fuzzy bounded linear functionals on $r$-fuzzy normedlinear spaces is obtained.

We prove that every continuous linear functional on the space S(R) consisting of the entire analytic functions whose Fourier transforms belong to the Schwartz space D has a unique minimal carrier cone in R, which substitutes for the support. The proof is based on a relevant decomposition theorem for elements of the spaces S(K) associated naturally with closed cones K ⊂ R. These results, essenti...

In previous work, Dietz and Sethuraman (2005), large deviations with respect to additive functionals were established for a class of finite-state time-nonhomogeneous Markov chains whose connecting transition matrices {Pn} converge to a general limit matrix P which includes some stochastic optimization algorithms. In this note, large deviations at the next level, that is with respect to K-word e...

We show that the mean inverse populations of nondecreasing, square integrable, continuous-time branching processes decrease to zero like the inverse of their mean population if and only if the initial population k is greater than a first threshold m1 ≥ 1. If, furthermore, k is greater than a second threshold m2 ≥ m1, the normalized mean inverse population is at most 1/(k −m2). We express m1 and...

We employ positivity of Riesz functionals to establish representing measures (or approximate representing measures) for truncated multivariate moment sequences. For a truncated moment sequence y, we show that y lies in the closure of truncated moment sequences admitting representing measures supported in a prescribed closed set K ⊆ R if and only if the associated Riesz functional Ly is K-positi...

In this lecture it is proposed to outline an abstract theory of functionals, with a development paralleling that of the theory of functions of real variables, and including also a chapter on analytic functionals. In Part II , some applications of the general theory to various sorts of equations are indicated. From the abstract point of view, the functional calculus is a form of general analysis...