We nd a Gaussian oo-diagonal heat kernel estimate for uniformly elliptic operators with measurable coeecients acting on regions R N , where the order 2m of the operator satisses N < 2m. The estimate is expressed using certain Riemannian-type metrics, and a geometrical result is established allowing conversion of the estimate into terms of the usual Riemannian metric on. Work of Barbatis 1] is a...

Composition operators C− between Orlicz spaces L.;6;1⁄4/ generated by measurable and nonsingular transformations − from  into itself are considered. We characterize boundedness and compactness of the composition operator between Orlicz spaces in terms of properties of the mapping − , the function ' and the measure space .;6;1⁄4/. These results generalize earlier results known for L p-spaces....

For f in L∞, the space of essentially bounded Lebesgue measurable functions on the unit circle, ∂D, the Toeplitz operator with symbol f is the operator Tf on the Hardy space H2 of the unit circle defined by Tfh = P (fh). Here P denotes the orthogonal projection in L2 with range H2. There are many fascinating problems about Toeplitz operators ([3], [6], [7] and [20]). In this paper we shall conc...

We justify the linear response theory for an ergodic Schrödinger operator with magnetic field within the non-interacting particle approximation, and derive a Kubo formula for the electric conductivity tensor. To achieve that, we construct suitable normed spaces of measurable covariant operators where the Liouville equation can be solved uniquely. If the Fermi level falls into a region of locali...

The p-norm of the Hilbert transform is the same as the p-norm of its truncation to any Lebesgue measurable set with strictly positive measure. This fact follows from two symmetry properties, the joint presence of which is essentially unique to the Hilbert transform. Our result applies, in particular, to the finite Hilbert transform taken over ( — 1,1), and to the one-sided Hilbert transform tak...

This paper settles the existence question for a rather general class of convex optimal design problems with a volume constraint. In low dimensions, we prove the existence of an optimal configuration for general convex minimization problems ruled by bounded measurable degenerate elliptic operators. Under a mild continuity assumption on the medium, the free boundary is proven to enjoy the appropr...

In this paper, we provide a notion of structure preserving maps (i.e. knowledge-belief morphisms) between knowledge-belief spaces. Then we show that under the condition that the knowledge operators of the players in a knowledge-belief space operate only on measurable subsets of the space there is a unique (up to isomorphism) universal knowledge-belief space to which every knowledge-belief space...

Let (,) be a measurable space with -finite continuous measure, ()=. A linear operator T:L1()+L()L1()+L() is called the Dunford-Schwartz if ||T(f)||1||f||1 (respectively, ||T(f)||||f||) for all fL1() fL()). {Tt}t0is strongly in L1() semigroup of operators, then each At(f)=1t∫0tTs(f)ds∈L1(Ω){{{A_t(f)} ={\frac{1}{t}} {\int_0^t} {T_s(f)} ds \in L_1(\Omega)}} has unique extension to operator, which ...

This paper studies second order elliptic equations in both divergence and non-divergence forms with measurable complex valued principle coefficients potentials. The PDE operators can be considered as generalized Schrodinger operators. Under some sufficient conditions, we prove existence, uniqueness, regularity estimates Sobolev spaces for solutions to the equations. We particularly show that no...

Using multiplicative ergodic theory we prove two formulae describing the relationships between different joint spectral radii for sets of bounded linear operators acting on a Banach space. In particular we recover a formula recently proved by V. S. Shulman and Yu. V. Turovskĭı using operatortheoretic ideas. As a byproduct of our method we answer a question of J. E. Cohen on the limiting behavio...