A major obstacle in extending the theory of well-bounded operators to cover operators whose spectrum is not necessarily real has been the lack of a suitable variation norm applicable to functions defined on an arbitrary nonempty compact subset σ of the plane. In this paper we define a new Banach algebra BV (σ) of functions of bounded variation on such a set and show that the function theoretic ...

(i) The integral of a non-negative extended real-valued measurabele function f on R d is given by R d f (x)dx = sup g R d g(x)dx where the supremum is taken over all bounded functions 0 ≤ g ≤ f which are bounded and supported on a set of finite measure. (ii) First suppose α < −n, and define a strictly decreasing sequence x m 0. We define step functions g n as follows. Define the sets A m = B xm...

Combining rearrangement techniques with Gromov’s proof (via optimal mass transportation) of the 1-Sobolev inequality, we prove a sharp quantitative version of the anisotropic Sobolev inequality on BV (R). As a corollary of this result, we also deduce a sharp stability estimate for the anisotropic 1-log-Sobolev inequality.

Abstract. A lower bound on the misclassification probability for a finite number of classes is obtained in terms of the total variation norms of the differences between the sub-distributions over the classes. This bound, which is shown to be exact in a certain rather strong sense, is based on an exact upper bound on the difference between the maximum and the mean of a finite set of real numbers...

We introduce the Bounded Axiom A Forcing Axiom(BAAFA). It turns out that it is equiconsistent with the existence of a regular Σ2-correct cardinal and hence also equiconsistent with BPFA. Furthermore we show that, if consistent, it does not imply the Bounded Proper Forcing Axiom(BPFA).

in this paper, the concept of {sl local base with  stratifiedstructure} in $i$-topological vector spaces is introduced. weprove that every $i$-topological vector space has a balanced localbase with stratified structure. furthermore, a newcharacterization of $i$-topological vector spaces by means of thelocal base with stratified structure is given.

We give several related versions of global Grothendieck Duality for unbounded complexes on noetherian formal schemes. The proofs, based on a nontrivial adaptation of Deligne’s method for the special case of ordinary schemes, are reasonably self-contained, modulo the Special Adjoint Functor Theorem. An alternative approach, inspired by Neeman and based on recent results about “Brown Representabi...

This work proposes a new methodology for establishing the tractability of a reasoning service that deals with expressive first-order knowledge bases. It consists of defining a logic that is weaker than classical logic and that has two properties: first, the entailment problem can be reduced to the model checking problem for a small number of characteristic models; and second, the model checking...

An efficient and high-order algorithm for three-dimensional bounded obstacle scattering is developed. The method is a non-trivial extension of recent work of the authors for two-dimensional bounded obstacle scattering, and is based on a boundary perturbation technique coupled to a well-conditioned high-order spectral-Galerkin solver. This boundary perturbation approach is justified by rigorous ...

In this paper, we introduce the notion of a bounded-parameter Markov decision process (BMDP) as a generalization of the familiar exact MDP. A bounded-parameter MDP is a set of exact MDPs specified by giving upper and lower bounds on transition probabilities and rewards (all the MDPs in the set share the same state and action space). BMDPs form an efficiently solvable special case of the already...