In the setting of adjoint pairs of operators we consider the question: to what extent does the Weyl M -function see the same singularities as the resolvent of a certain restriction AB of the maximal operator? We obtain results showing that it is possible to describe explicitly certain spaces S and S̃ such that the resolvent bordered by projections onto these subspaces is analytic everywhere that...

Let T (t), 0 ≤ t < ∞, be a one parameter c0-semigroup of bounded linear operators on a Banach space X with infinitesimal generator A and R(λ, A) be the resolvent operator of A. The Hille-Yosida Theorem for c0-semigroups asserts that the resolvent operator of the infinitesimal generator A satisfies ‖R(λ, A)‖ ≤ M λ−ω for some constants M > 0 and λ ∈ R (the set of real numbers), λ > ω. The object ...

For any univariate polynomial P whose coefficients lie in an ordinary differential field F of characteristic zero, and for any constant indeterminate α, there exists a nonunique nonzero linear ordinary differential operator R of finite order such that the αth power of each root of P is a solution of Rzα = 0, and the coefficient functions of R all lie in the differential ring generated by the co...

We consider the Stokes resolvent problem in a two-dimensional bounded Lipschitz domain $\Omega$ subject to homogeneous Dirichlet boundary conditions. prove $\mathrm{L}^p$-resolvent estimates for $p$ satisfying condition $\lvert 1 / p - 2 \rvert < 4 + \varepsilon$ some $\varepsilon > 0$. further show that operator admits property of maximal regularity and its $\mathrm{H}^{\infty}$-calculus is bo...

In this paper, we introduce and consider a new system of extended general variational inclusions involving eight different operators. Using the resolvent operator techniques, we show that the new system of extended general variational inclusions is equivalent to the fixed point problem. We prove the strong convergence of some new explicit iterative parallel algorithms using resolvent methods un...

We study the asymptotic behaviour of the powers T of a composition operator T on an arbitrary Banach space X of holomorphic functions on the open unit disc D of C. We show that for composition operators, one has the following dichotomy: either the powers converge uniformly or they do not converge even strongly. We also show that uniform convergence of the powers of an operator T ∈ L(X) is very ...

The resolvent operator approach is applied to address a system of generalized ordered variational inclusions with ⊕ operator in real ordered Banach space. With the help of the resolvent operator technique, Li et al. (J. Inequal. Appl. 2013:514, 2013; Fixed Point Theory Appl. 2014:122, 2014; Fixed Point Theory Appl. 2014:146, 2014; Appl. Math. Lett. 25:1384-1388, 2012; Fixed Point Theory Appl. 2...