Symmetric Operators with Twice Continuously Differentiable Spectral Functions
نویسندگان
چکیده
منابع مشابه
Modelling with twice continuously differentiable functions ∗
Many real life situations can be described using twice continuously differentiable functions over convex sets with interior points. Such functions have an interesting separation property: At every interior point of the set they separate particular classes of quadratic convex functions from classes of quadratic concave functions. Using this property we introduce new characterizations of the deri...
متن کاملTwice Differentiable Spectral Functions
A function F on the space of n × n real symmetric matrices is called spectral if it depends only on the eigenvalues of its argument. Spectral functions are just symmetric functions of the eigenvalues. We show that a spectral function is twice (continuously) differentiable at a matrix if and only if the corresponding symmetric function is twice (continuously) differentiable at the vector of eige...
متن کاملMultiplicative character sums with twice-differentiable functions
For a nontrivial multiplicative character χ modulo p, we bound character sums Sf (χ;N) = N ∑ n=1 χ(⌊f(n)⌋) taken on the integer parts of a real-valued, twice-differentiable function f whose second derivative decays at an appropriate rate. For the special case that f(x) = xη with some positive real number η, our bounds extend recent results of several authors. Mathematics Subject Classification ...
متن کاملOn the functional form of convex underestimators for twice continuously differentiable functions
The optimal functional form of convex underestimators for general twice continuously differentiable functions is of major importance in deterministic global optimization. In this paper, we provide new theoretical results that address the classes of optimal functional forms for the convex underestimators. These are derived based on the properties of shift-invariance and sign-invariance.
متن کاملSome Jensen’s Type Inequalities for Twice Differentiable Functions of Selfadjoint Operators in Hilbert Spaces
Some Jensen’s type inequalities for twice differentiable functions of selfadjoint operators in Hilbert spaces under suitable assumptions for the involved operators are given. Applications for particular cases of interest are also provided.
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: 1969
ISSN: 0002-9939
DOI: 10.2307/2037171