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Results tagged with ca.classical-analysis-and-odes
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user 8857
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
0
votes
Accepted
When a set of measure zero plus itself contains interior
Regarding Question #1.
There's one obvious dimensional obstruction (for example consider the Hausdorff dimension of A).
There is some research about it in the 1-dimensional case, such as the well-kn …
- 2,459
7
votes
Background for Hejhal's "The Selberg Trace Formula for $PSL(2, \mathbb{R})$
Well, the modern viewpoint relays on the interpretation of "fourier transform" (in any generalized fashion you like to define "fourier transform") in representation-theoretic language.
As a consequenc …
- 2,459
8
votes
Applications of measure, integration and Banach spaces to combinatorics
Fourier Analysis is a major tool in Arithmetic combinatorics (see Tao and Vu's book, they have a chapter named L^p theory, i.e. the theorem of Bourgain's about "long APs in sumsets").
Moreover, one c …
- 2,459
5
votes
Uniform distribution of sequence mod 1
It is unclear what is "most $r$'s even mean.
A standard argument would show that for any increasing sequence, for Lebesgue almost every $x$, $a_{n}.x$ is equidistributed mod $1$.
For the case of power …
- 2,459
5
votes
Kronecker Approximation theorem and Fibonacci numbers
You've received two good answers, but I'll elaborate a bit.
Usually equidistribution on the torus (or more general, compact groups) wrt the Haar measure is achieved by computing the Weyl sums and show …
- 2,459