Displaying similar documents to “Remark to the comparison of solution properties of Love's equation with those of wave equation”

Norm estimates of discrete Schrödinger operators

Ryszard Szwarc (1998)

Colloquium Mathematicae


Harper’s operator is defined on 2 ( Z ) by H θ ξ ( n ) = ξ ( n + 1 ) + ξ ( n - 1 ) + 2 cos n θ ξ ( n ) , where θ [ 0 , π ] . We show that the norm of H θ is less than or equal to 2 2 for π / 2 θ π . This solves a conjecture stated in [1]. A general formula for estimating the norm of self-adjoint tridiagonal infinite matrices is also derived.

New variants of Khintchine's inequality.

Ioan Serb (2001)

Collectanea Mathematica


Variants of Khintchine's inequality with coefficients depending on the vector dimension are proved. Equality is attained for different types of extremal vectors. The Schur convexity of certain attached functions and direct estimates in terms of the Haagerup type of functions are also used.