In this paper, we give the definition of local variable Morrey–Lorentz spaces Mp(⋅),q(⋅),λloc(Rn) which are a new class functions. Also, prove boundedness Hardy–Littlewood maximal operator M and Calderón–Zygmund operators T on these spaces. Finally, apply results to Bochner–Riesz Brδ, identity approximation Aε Marcinkiewicz μΩ Mp(⋅),q(⋅),λloc(Rn).

Let H1 and H2 be Hilbert spaces and let B(H1,H2) be the space of bounded linear operators A : H1 → H2. An operator A ∈ B(H1,H2) is said to be Fredholm if first, the kernel ofA is finite-dimensional, and second the image ofA is closed and has finite codimension. An application of the open mapping theorem shows that the closedness requirement on the image is redundant. A well-known example of Fre...

In this paper second order elliptic boundary value problems on bounded domains Ω ⊂ Rn with boundary conditions on ∂Ω depending nonlinearly on the spectral parameter are investigated in an operator theoretic framework. For a general class of locally meromorphic functions in the boundary condition a solution operator of the boundary value problem is constructed with the help of a linearization pr...

We regard the Schrr odinger{Poisson system arising from the modelling of an electron gas with reduced dimension in a bounded up to three{ dimensional domain and establish the method of steepest descent. The electro-static potentials of the iteration scheme will converge uniformly on the spatial domain. To get this result we investigate the Schrr odinger operator, the Fermi level and the quantum...

Let R denote a domain in C with boundary B. Let X denote the closure of R. An operator T on a complex Hilbert space H has X as a spectral set if σ(T ) ⊂ X and ‖f(T )‖ ≤ ‖f‖R = sup{|f(z)| : z ∈ R} for every rational function f with poles off X. The expression f(T ) may be interpreted either in terms of the Riesz functional calculus, or simply by writing the rational function f as pq−1 for polyno...

Abstract In this work, we study the existence, uniqueness, and continuous dependence of solutions for a class fractional differential equations by using generalized Riesz operator. One can view results work as refinement existence theory with Riemann–Liouville, Caputo, classical derivative. Some special cases be derived to obtain corresponding equations. We provide an illustrated example unique...

We use Operator Ideals Theory and Gershgorin theory to obtain explicit information in terms of the symbol concerning spectrum pseudo-differential operators, on a smooth manifold ? with boundary ? , context non-harmonic analysis value problems introduced [29] model operator L. For symbols Hörmander class S 1 0 ( ¯ × I ) we provide version Gohberg's lemma, sufficient necessary condition ensure th...

For Maxwell operators in Lipschitz domains, we describe all m-dissipative boundary conditions and apply this result to generalized impedance Leontovich including the cases of singular, degenerate, randomized coefficients. To end construct Riesz bases trace spaces associated with curl-operator introduce a modified version triple adapted specifics equations, namely, mixed-order duality related sp...

Abstract We solve the closed range problem for Volterra-type integral operator on Fock spaces. Several applications of result related to operators invertibility, Fredholm, and dynamical sampling structures from frame perspectives are provided. further prove a bounded preserves no property. On contrary, adjoint if only it is noncompact but fails preserve both tight frames Riesz basis.

Abstract In this paper, the Riesz-Caputo fractional derivative of variable order with fixed memory is considered. The studied non-integer differential operator approximated by means modified basic rules numerical integration. three proposed methods are based on polynomial interpolation: piecewise constant, linear, and quadratic interpolation. errors generated described experimental rate converg...