We give an overview of the generalized Calderón-Zygmund theory for “non-integral” singular operators, that is, operators without kernels bounds but appropriate off-diagonal estimates. This theory is powerful enough to obtain weighted estimates for such operators and their commutators with BMO functions. L − L off-diagonal estimates when p ≤ q play an important role and we present them. They are...

We give an overview of the generalized Calderón-Zygmund theory for “non-integral” singular operators, that is, operators without kernels bounds but appropriate off-diagonal estimates. This theory is powerful enough to obtain weighted estimates for such operators and their commutators with BMO functions. L − L off-diagonal estimates when p ≤ q play an important role and we present them. They are...

Let Pf(x) = −if ′(x) and Qf(x) = xf(x) be the canonical operators acting on an appropriate common dense domain in L2(R). The derivations DP (A) = i(PA−AP ) and DQ(A) = i(QA−AQ) act on the ∗-algebra A of all integral operators having smooth kernels of compact support, for example, and one may consider the noncommutative “Laplacian” L = D2 P + D 2 Q as a linear mapping of A into itself. L generat...

For a quantum Markov semigroup T on the algebra B(h) with a faithful invariant state ρ, we can define an adjoint T̃ with respect to the scalar product determined by ρ. In this paper, we solve the open problems of characterising adjoints T̃ that are also a quantum Markov semigroup and satisfy the detailed balance condition in terms of the operators H,Lk in the Gorini Kossakowski Sudarshan Lindblad...

In this paper, we investigate spectral properties of explosive symmetric Markov processes. Under a condition on its life time, prove the $L^1$-semigroup processes become compact operators.

We investigate the solution of an N-unit series system with finite number of vacations. By using CC00-semigroup theory of linear operators, we prove well-posedness and the existence of the unique positive dynamic solution of the system.

In this work, we prove the existence and uniqueness of solution generalized Schrödinger equation in periodic distributional space P’. Furthermore, that depends continuously respect to initial data Introducing a family weakly continuous operators, is semigroup operators Then, with get fine version dependency theorem obtained. Finally, provide some consequences study.