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Compression of slant Toeplitz operators on the Hardy space of n -dimensional torus

Gopal Datt, Shesh Kumar Pandey (2020)

Czechoslovak Mathematical Journal

This paper studies the compression of a k th-order slant Toeplitz operator on the Hardy space H 2 ( 𝕋 n ) for integers k ≥ 2 and n ≥ 1 . It also provides a characterization of the compression of a k th-order slant Toeplitz operator on H 2 ( 𝕋 n ) . Finally, the paper highlights certain properties, namely isometry, eigenvalues, eigenvectors, spectrum and spectral radius of the compression of k th-order slant Toeplitz operator on the Hardy space H 2 ( 𝕋 n ) of n -dimensional torus 𝕋 n .

Computation of topological degree in ordered Banach spaces with lattice structure and applications

Yujun Cui (2013)

Applications of Mathematics

Using the cone theory and the lattice structure, we establish some methods of computation of the topological degree for the nonlinear operators which are not assumed to be cone mappings. As applications, existence results of nontrivial solutions for singular Sturm-Liouville problems are given. The nonlinearity in the equations can take negative values and may be unbounded from below.

Computing the differential of an unfolded contact diffeomorphism

Klaus Böhmer, Drahoslava Janovská, Vladimír Janovský (2003)

Applications of Mathematics

Consider a bifurcation problem, namely, its bifurcation equation. There is a diffeomorphism Φ linking the actual solution set with an unfolded normal form of the bifurcation equation. The differential D Φ ( 0 ) of this diffeomorphism is a valuable information for a numerical analysis of the imperfect bifurcation. The aim of this paper is to construct algorithms for a computation of D Φ ( 0 ) . Singularity classes containing bifurcation points with c o d i m ≤ 3 , c o r a n k = 1 are considered.

Computing the numerical range of Krein space operators

Natalia Bebiano, J. da Providência, A. Nata, J.P. da Providência (2015)

Open Mathematics

Consider the Hilbert space (H,〈• , •〉) equipped with the indefinite inner product[u,v]=v*J u,u,v∈ H, where J is an indefinite self-adjoint involution acting on H. The Krein space numerical range WJ(T) of an operator T acting on H is the set of all the values attained by the quadratic form [Tu,u], with u ∈H satisfying [u,u]=± 1. We develop, implement and test an alternative algorithm to compute WJ(T) in the finite dimensional case, constructing 2 by 2 matrix compressions of T and their easily determined...

Concave iteration semigroups of linear continuous set-valued functions

Andrzej Smajdor, Wilhelmina Smajdor (2012)

Open Mathematics

Let F t: t ≥ 0 be a concave iteration semigroup of linear continuous set-valued functions defined on a convex cone K with nonempty interior in a Banach space X with values in cc(K). If we assume that the Hukuhara differences F 0(x) − F t (x) exist for x ∈ K and t > 0, then D t F t (x) = (−1)F t ((−1)G(x)) for x ∈ K and t ≥ 0, where D t F t (x) denotes the derivative of F t (x) with respect to t and G ( x ) = lim s → 0 F 0 x - F s x F 0 x - F s x - s - s for x ∈ K.

Concave iteration semigroups of linear set-valued functions

Jolanta Olko (1999)

Annales Polonici Mathematici

We consider a concave iteration semigroup of linear continuous set-valued functions defined on a closed convex cone in a separable Banach space. We prove that such an iteration semigroup has a selection which is also an iteration semigroup of linear continuous functions. Moreover it is majorized by an "exponential" family of linear continuous set-valued functions.

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