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On some local spectral theory and bounded local resolvent of operator matrices

Abdelaziz Tajmouati, Abdeslam El Bakkali, Mohammed Karmouni (2018)

Mathematica Bohemica

We extend and generalize some results in local spectral theory for upper triangular operator matrices to upper triangular operator matrices with unbounded entries. Furthermore, we investigate the boundedness of the local resolvent function for operator matrices.

On some new spectral estimates for Schrödinger-like operators

Daniel Levin (2006)

Open Mathematics

We prove the analog of the Cwikel-Lieb-Rozenblum estimate for a wide class of second-order elliptic operators by two different tools: Lieb-Thirring inequalities for Schrödinger operators with matrix-valued potentials and Sobolev inequalities for warped product spaces.

On some nonlinear alternatives of Leray-Schauder type and functional integral equations

Bapurao Chandra Dhage (2006)

Archivum Mathematicum

In this paper, some new fixed point theorems concerning the nonlinear alternative of Leray-Schauder type are proved in a Banach algebra. Applications are given to nonlinear functional integral equations in Banach algebras for proving the existence results. Our results of this paper complement the results that appear in Granas et. al. (Granas, A., Guenther, R. B. and Lee, J. W., Some existence principles in the Caratherodony theory of nonlinear differential system, J. Math. Pures Appl. 70 (1991),...

On some problems connected with diagonal map in some spaces of analytic functions

Romi Shamoyan (2008)

Mathematica Bohemica

For any holomorphic function f on the unit polydisk 𝔻 n we consider its restriction to the diagonal, i.e., the function in the unit disc 𝔻 defined by Diag f ( z ) = f ( z , ... , z ) , and prove that the diagonal map Diag maps the space Q p , q , s ( 𝔻 n ) of the polydisk onto the space Q ^ p , s , n q ( 𝔻 ) of the unit disk.

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