In this paper, we obtain the regularized trace formulae for a diffusion operator, which includes conformable fractional derivatives of order ? (0 < 1) instead ordinary in traditional operator by contour integration method. The results paper are great importance solving inverse problems and can be considered as partial generalizations.

Let L be a Schrödinger operator of the form = − Δ + V acting on 2 ( R n ) where nonnegative potential belongs to reverse Hölder class B q for some ≥ . BMO denote space associated L. In this article we will show that function f ∈ is trace solution u : t 0 , x satisfies Carleson-type condition sup r ∫ | ∂ ∇ d ≤ C < ∞ Conversely, characterizes all L-carolic functions whose traces belong

In addition to Pisier’s counterexample of a non-accessible maximal Banach ideal, we will give a large class of maximal Banach ideals which are accessible. The first step is implied by the observation that a ”good behaviour” of trace duality, which is canonically induced by conjugate operator ideals can be extended to adjoint Banach ideals, if and only if these adjoint ideals satisfy an accessib...

It was shown in [2] that if T is a contraction in a Hilbert space with finite defect (‖T‖ ≤ 1, rank(I−T ∗T ) <∞), and its spectrum σ(T ) doesn’t coincide with the closed unit disk D, then the following Linear Resolvent Growth condition ‖(λI − T )−1‖ ≤ C dist(λ, σ(T )) , λ ∈ C\σ(T ), implies that T is similar to a normal operator. The condition rank(I − T ∗T ) < ∞ characterizes how close is T to...

In this work, a formula for the regularized trace of second order differential operator given in a finite interval which has unbounded operator coefficients is found.

Abstract We provide a countable set of conditions based on elementary symmetric polynomials that are necessary and sufficient for trace class integral operator to be positive semidefinite, which is an important cornerstone quantum theory in phase-space representation. also present new, efficiently computable algorithm Newton’s identities. Our test positivity much more sensitive than the ones gi...

A new approach to boundary trace inequalities for Sobolev functions is presented, which reduces any trace inequality involving general rearrangement-invariant norms to an equivalent, considerably simpler, one-dimensional inequality for a Hardy-type operator. In particular, improvements of classical boundary trace embeddings and new optimal trace embeddings are derived.

Zinc, an essential trace element, plays indispensable roles in multiple cellular processes.[...].