On the Friedrichs Operator
نویسندگان
چکیده
^Let ii be a simply connected domain in C1 with the area measure dA . Let Pa be the orthogonal projection from L?(Q.,dA) onto the closed subspace of antiholomorphic functions in L2(Í2, dA). The Friedrichs operator Tçi associated to Í2 is the operator from the Bergman space L*(Q.) into L2(fi, dA) defined by Tnf = Paf. In this note, some smoothness conditions on the boundary of Í2 are given such that the Friedrichs operator 7q belongs to the Schatten classes Sp .
منابع مشابه
Friedrichs Model Operators of Absolute Type with One Singular Point
Problems of existence of the singular spectrum on the continuous spectrum emerges in some mathematical aspects of quantum scattering theory and quantum solid physics. In the latter field, this phenomenon results from physical effects such as the Anderson transitions in dielectrics. In the study of this problem, selfadjoint Friedrichs model operators play an important part and constitute quite a...
متن کاملSome Spectral Properties of the Non-self-adjoint Friedrichs Model Operator
A non-self-adjoint, rank-one Friedrichs model operator in L2(R) is considered in the case where the determinant of perturbation is an outer function in the half-planes C±. Its spectral structure is investigated. The impact of the linear resolvent growth condition on its spectral properties (including the similarity problem) is studied.
متن کاملOn the Stability of Friedrichs' Scheme and the Modified Lax-Wendroff Scheme*
Necessary and sufficient stability criteria for Friedrichs' scheme and the modified Lax-Wendroff scheme with smooth coefficients are derived by means of Kreiss' Matrix Theorem and the first Stability Theorem of Lax and Nirenberg. In this note we derive necessary and sufficient stability criteria for Friedrichs' scheme and the modified Lax-Wendroff scheme [8] for the hyperbolic system n (1) ". =...
متن کاملThe Correct Use of the Lax – Friedrichs Method ∗
We are concerned with the structure of the operator corresponding to the Lax–Friedrichs method. At first, the phenomenae which may arise by the naive use of the Lax–Friedrichs scheme are analyzed. In particular, it turns out that the correct definition of the method has to include the details of the discretization of the initial condition and the computational domain. Based on the results of th...
متن کاملAn Intrinsic Criterion for the Bijectivity of Hilbert Operators Related to Friedrichs’ Systems
Friedrichs’ theory of symmetric positive systems of first-order PDE’s is revisited so as to avoid invoking traces at the boundary. Two intrinsic geometric conditions are introduced to characterize admissible boundary conditions. It is shown that the space in which admissible boundary conditions can be enforced is maximal in a positive cone associated with the differential operator. The equivale...
متن کامل