Tags » Math.CA

Quantitative continuity estimates

Suppose is a continuous (but nonlinear) map from one normed vector space to another . The continuity means, roughly speaking, that if are such that is small, then is also small (though the precise notion of “smallness” may depend on or , particularly if is not known to be… 1,896 more words


Generalisations of the limit functional

Suppose one has a bounded sequence of real numbers. What kinds of limits can one form from this sequence?

Of course, we have the usual notion of limit , which in this post I will refer to as the… 1,421 more words


Notes on nilcharacters and their symbols

A sequence of complex numbers is said to be quasiperiodic if it is of the form

for some real numbers and continuous function . For instance, linear phases such as (where ) are examples of quasiperiodic sequences; the top order coefficient (modulo ) can be viewed as a “frequency” of the integers, and an element of the… 4,730 more words


Yves Meyer wins the 2017 Abel Prize

Just a short post to note that Norwegian Academy of Science and Letters has just announced that the 2017 Abel prize has been awarded to Yves Meyer… 352 more words


Math 246A, Notes 4: singularities of holomorphic functions

In the previous set of notes we saw that functions that were holomorphic on an open set enjoyed a large number of useful properties, particularly if the domain was simply connected. 11,838 more words


246A, Notes 1: complex differentiation

At the core of almost any undergraduate real analysis course are the concepts of differentiation and integration, with these two basic operations being tied together by the… 6,476 more words