منابع مشابه
Analytic Functions of M-Matrices and Generalizations
We introduce the notion of positivity cone K of matrices in enn and with such a K we associate sets Z and M. For suitable choices of K the set M consists of the classical (non-singular) M-matrices or of the positive definite (Hermitian) matrices. If A EM and I .;; p " 3 we prove that there is a unique B EM for which BP = A . If P > 3, this uniqueness theorem is false for general M and we prove ...
متن کاملFrom random matrices to random analytic functions
Singular points of random matrix-valued analytic functions are a common generalization of eigenvalues of random matrices and zeros of random polynomials. The setting is that we have an analytic function of z taking values in the space of n× n matrices. Singular points are those (random) z where the matrix becomes singular, that is, the zeros of the determinant. This notion was introduced in the...
متن کاملSingular values of convex functions of matrices
Let $A_{i},B_{i},X_{i},i=1,dots,m,$ be $n$-by-$n$ matrices such that $sum_{i=1}^{m}leftvert A_{i}rightvert ^{2}$ and $sum_{i=1}^{m}leftvert B_{i}rightvert ^{2}$ are nonzero matrices and each $X_{i}$ is positive semidefinite. It is shown that if $f$ is a nonnegative increasing convex function on $left[ 0,infty right) $ satisfying $fleft( 0right) =0 $, then $$2s_{j}left( fleft( fra...
متن کاملA Subclass of Analytic Functions Associated with Hypergeometric Functions
In the present paper, we have established sufficient conditions for Gaus-sian hypergeometric functions to be in certain subclass of analytic univalent functions in the unit disc $mathcal{U}$. Furthermore, we investigate several mapping properties of Hohlov linear operator for this subclass and also examined an integral operator acting on hypergeometric functions.
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: Proceedings of the American Mathematical Society
سال: 1960
ISSN: 0002-9939
DOI: 10.2307/2032724