Analysis called Hypercontractivity. We shall see the theorem and a few of its ... Hypercontractivity. Even the q-th norm of Tρ(f ) is smaller than the p-th ...

The notion of hypercontractivity first arose in quantum field theory [3] and underwent much development in functional analysis and mathematical physics.

The hypercontractivity theorem says that Tρ is actually a hypercontractive map, in that it smooths out f even when one measures Tρf in a higher norm. With ...

Mar 8, 2007 · The idea behind the statement is that the Tρ operator smooths, or “reasonable-izes”, functions. Theorem 1.1 (Hypercontractivity Theorem.) ...

Feb 15, 2010 · Hypercontractive inequalities are a useful tool in dealing with extremal questions in the geometry of high-dimensional discrete and continuous ...

Jan 31, 2023 · In this lecture, we overview the theory of hypercontractivity and its applications to understand- ing expansion of higher order random walks ...

For the past twenty years, a set of ideas known as hypercontractivity has played a continuing role in analysis with ramifications in quantum field theory, self- ...

The hypercontractivity theorem says that Tρ is actually a hypercontractive map, in that it smooths out f even when one measures Tρf in a higher norm. With ...

The hypercontractivity theorem gives the reverse inequality when we add some noise. ... The hypercontrac- tive inequality controls the relation between the two.

Jul 3, 2023 · This hypercontractive inequality is not sharp, which precludes applications to the symmetric group S_n and to other settings where sharpness of ...