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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

1 vote
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About the exponential bounds for modified Bessel function

There are some bounds of that form in this paper. See also the first reference at the end of the paper.
John D. Cook's user avatar
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3 votes

The mean of points on a unit n-sphere $S^n$

I think what you're looking for is the field of statistics known as directional statistics. Even for the circle $S^1$ it's not obvious how things should be defined, but it is possible, depending on co …
John D. Cook's user avatar
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5 votes

Good books on theory of distributions

Robert Adams' Sobolev Spaces. Maybe not the best first book, but a very good second book.
10 votes

A good book of functional analysis

I'd recommend the Dunford and Schwartz. It's a classic. It's huge -- three volumes. But you don't have to read the whole series cover-to-cover. If you read half of the first volume, you'll learn about …
41 votes

Why do we care about $L^p$ spaces besides $p = 1$, $p = 2$, and $p = \infty$?

In PDEs, various values of p arise as degrees of regularity. The Sobolev embedding theorems let you "trade in" generalized derivatives for classical derivatives. You might need the exponent p to be …