Functional Inequalities in Analysis and Probability Theory
نویسنده
چکیده
My research is in Functional Analysis (AMS classification 46), Operator Theory (47), Global Analysis (58), Probability Theory (60), and Combinatorics (05). Most of what I do relates to functional inequalities, often arising in mathematical physics, in many different contexts. Much of my recent work is in and around free probability theory, an important and relatively new field at the confluence of operator algebras, combinatorics, and probability theory.
منابع مشابه
Acceptable random variables in non-commutative probability spaces
Acceptable random variables are defined in noncommutative (quantum) probability spaces and some of probability inequalities for these classes are obtained. These results are a generalization of negatively orthant dependent random variables in probability theory. Furthermore, the obtained results can be used for random matrices.
متن کاملNew inequalities for a class of differentiable functions
In this paper, we use the Riemann-Liouville fractionalintegrals to establish some new integral inequalities related toChebyshev's functional in the case of two differentiable functions.
متن کاملSome functional inequalities in variable exponent spaces with a more generalization of uniform continuity condition
Some functional inequalities in variable exponent Lebesgue spaces are presented. The bi-weighted modular inequality with variable exponent $p(.)$ for the Hardy operator restricted to non- increasing function which is$$int_0^infty (frac{1}{x}int_0^x f(t)dt)^{p(x)}v(x)dxleqCint_0^infty f(x)^{p(x)}u(x)dx,$$ is studied. We show that the exponent $p(.)$ for which these modular ine...
متن کاملQuadratic $rho$-functional inequalities in $beta$-homogeneous normed spaces
In cite{p}, Park introduced the quadratic $rho$-functional inequalitiesbegin{eqnarray}label{E01}&& |f(x+y)+f(x-y)-2f(x)-2f(y)| \ && qquad le left|rholeft(2 fleft(frac{x+y}{2}right) + 2 fleft(frac{x-y}{2}right)- f(x) - f(y)right)right|, nonumberend{eqnarray}where $rho$ is a fixed complex number with $|rho|
متن کاملConcentration of Measure Inequalities in Information Theory, Communications and Coding (Second Edition)
Concentration inequalities have been the subject of exciting developments during the last two decades, and have been intensively studied and used as a powerful tool in various areas. These include convex geometry, functional analysis, statistical physics, mathematical statistics, pure and applied probability theory (e.g., concentration of measure phenomena in random graphs, random matrices, and...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007