Regularity Theorems and Optimal Errors Estimates for Linear Parabolic Cauchy Problems.
Regularization of Some Classes of Ultradistribution Semigroups and Sines
Regularized cosine existence and uniqueness families for second order abstract Cauchy problems
Let (i = 1,2) be two arbitrary bounded operators on a Banach space. We study (C₁,C₂)-regularized cosine existence and uniqueness families and their relationship to second order abstract Cauchy problems. We also prove some of their basic properties. In addition, Hille-Yosida type sufficient conditions are given for the exponentially bounded case.
Regularized semigroups and systems of linear partial differential equations
Regularized Semigroups, Iterated Cauchy Problems and Equipartition of Energy.
Relative boundedness and compactness theory for second-order differential operators.
Remarks on Ordinary Differential Equations in Orderd Banach Spaces.
Resolvent and spectrum of a nonselfadjoint differential operator in a Hilbert space
We consider a second order regular differential operator whose coefficients are nonselfadjoint bounded operators acting in a Hilbert space. An estimate for the resolvent and a bound for the spectrum are established. An operator is said to be stable if its spectrum lies in the right half-plane. By the obtained bounds, stability and instability conditions are established.