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Results tagged with ca.classical-analysis-and-odes
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user 147078
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
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$L^p$ norm of Fourier transform of function composed with a diffeomorphism
Suppose $f$ is a compactly supported smooth function from $\mathbb{R}^n$ to $\mathbb{C}$ and $A$ is a diffeomorphism on $\mathbb{R}^n$, do we have any theorems relating the $L^p$ norm of $\hat{f}$ and …
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Notation for right hand side of local smoothing conjecture
In Tao's "Recent progress on the restriction conjecture"
On page 53, Tao introduced the local smoothing conjecture: let $u(t,x)$ be the solution to the wave equation $u_{tt}=\Delta u$, $u(0,x)=f(x)$ a …
- 265
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Use of Stein's maximal principle in Bourgain's paper on Besicovitch sets
I'm trying to understand Bourgain's paper "Besicovitch type maximal operators and applications to Fourier analysis". Let $\xi\in S^2\subset\mathbb{R}^3$ be a unit vector and $\delta>0$, by a $(\xi,\de …
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Fourier restriction in decoupling inequalities
I'm reading Bourgain and Demeter's paper https://arxiv.org/abs/1403.5335 "The proof of the $l^2$ decoupling conjecture".
On page 1 the paper says, let $P^{n-1}=\{(\xi_1,...,\xi_{n-1},\xi_1^2+...+\xi_{ …
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