The eigenvalue characterization for the constant sign Green’s functions of ( k , n − k ) $(k,n-k)$ problems

The eigenvalue Characterization for the constant Sign Green ’ s Functions of ( k , n − k ) problems

This paper is devoted to the study of the sign of the Green’s function related to a general linear n-order operator, depending on a real parameter, Tn[M ], coupled with the (k, n−k) boundary value conditions. If operator Tn[M̄ ] is disconjugate for a given M̄ , we describe the interval of values on the real parameter M for which the Green’s function has constant sign. One of the extremes of the i...

Polarization constant $mathcal{K}(n,X)=1$ for entire functions of exponential type

In this paper we will prove that if $L$ is a continuous symmetric n-linear form on a Hilbert space and $widehat{L}$ is the associated continuous n-homogeneous polynomial, then $||L||=||widehat{L}||$. For the proof we are using a classical generalized  inequality due to S. Bernstein for entire functions of exponential type. Furthermore we study the case that if X is a Banach space then we have t...

On the Rational Recursive Sequence X_{N+1}=ƔX_{N-K}+(AX_N+BX_{N-K})⁄(CX_N-DX_{N-K})

polarization constant $k(n,x)=1$ for entire functions of exponential type

in this paper we will prove that if $l$ is a continuous symmetric n-linear form on a hilbert spaceand $widehat{l}$ is the associated continuous n-homogeneous polynomial, then $||l||=||widehat{l}||$.for the proof we are using a classical generalized  inequality due to s. bernstein for entire functions of exponential type. furthermore we study the case that if x is a banach space then we have tha...

on the rational recursive sequence x_{n+1}=ɣx_{n-k}+(ax_n+bx_{n-k})⁄(cx_n-dx_{n-k})