On two functions of a matrix with positive definite hermitian part
نویسندگان
چکیده
منابع مشابه
Strictly Hermitian Positive Definite Functions
Let H be any complex inner product space with inner product < ·, · >. We say that f : | C → | C is Hermitian positive definite on H if the matrix ( f(< z,z >) )n r,s=1 (∗) is Hermitian positive definite for all choice of z, . . . ,z in H, all n. It is strictly Hermitian positive definite if the matrix (∗) is also non-singular for any choice of distinct z, . . . ,z in H. In this article we prove...
متن کاملMatrices with Positive Definite Hermitian Part : Inequalities and Linear
The Hermitian and skew-Hermitian parts of a square matrix A are deened by H(A) (A + A)=2 and S(A) (A ? A)=2: We show that the function f(A) = (H(A ?1)) ?1 is convex with respect to the Loewner partial order on the cone of matrices with positive deenite Hermitian part. That is, for any matrices A and B with positive deenite Hermitian part ff(A) + f(B)g=2 ? f(fA + Bg=2) is positive semideenite: U...
متن کاملRestricted Algebras on Inverse Semigroups - Part II: Positive Definite Functions
The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. In this paper, we investigate the concept of restricted positive definite functions and their relation with restricted representations of an inverse semigroup. We also introduce the restricted Fourier ...
متن کاملSome numerical radius inequalities with positive definite functions
Using several examples of positive definite functions, some inequalities for the numerical radius of matrices are investigated. Also, some open problems are stated.
متن کاملOn Matrix Valued Square Integrable Positive Definite Functions
In this paper, we study matrix valued positive definite functions on a unimodular group. We generalize two important results of Godement on L positive definite functions to matrix valued L positive definite functions. We show that a matrix-valued continuous L positive definite function can always be written as a convolution of a L positive definite function with itself. We also prove that, give...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1996
ISSN: 0024-3795
DOI: 10.1016/0024-3795(94)00208-8