Perturbation Quadratic Forms Of L p Contraction Semigroup

Abstract

A complex matrix is associated with a sequence of real numbers. The present study demonstrates the methodology for computing the actual perturbation values and highlights their resemblance to the singular values in terms of various properties. Real perturbation values can be utilized to compute the real pseudospectra and real stability radii. The primary outcome pertains to the signature exhibited by real quadratic forms within complex vector spaces.  In this work I showed a result of the contraction semigroup norm for vector-valued functions, the Markovian semigroup which is symmetric and not the only one on  contraction semigroup but also a  contraction of semigroup for any  and I prove that the sharp estimate of the defective logarithmic Sobolev inequality holds for