# Questions tagged [harmonic-analysis]

Harmonic analysis is a generalisation of Fourier analysis that studies the properties of functions. Check out this tag for abstract harmonic analysis (on abelian locally compact groups), or Euclidean harmonic analysis (eg, Littlewood-Paley theory, singular integrals). It also covers harmonic analysis on tube domains, as well as the study of eigenvalues and eigenvectors of the Laplacian on domains, manifolds and graphs.

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### Functions arising as STFT with band-limited window of a compactly supported function

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### Uniform distribution in a cancelling exponential sum

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### Half-integer Fourier transform

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### Spherical harmonics, $\frak{sl}_2$, and algebra gradings

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### Spherical harmonic expansion of a power function

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### Understanding the regular representation of an LCA group as a 'direct integral'

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### Generalization of Bernstein’s inequality

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### $L^2$ convergence of a particular function

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### $L^p$ estimate of a multiplier operator

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### Is the Besov space $B_{\infty,1}^0(\mathbb{R}^d)$ a multiplication algebra?

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### Haar measure coming from Pontryagin duality v/s Fourier inversion

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### Weak-type inequality for the partial Fourier sum operator

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### Analogous form of Hardy-Littlewood maximal inequality (weak/strong type) on affine subspaces

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### “Reversed” Bernstein Inequality

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### On inverting characteristic functions

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### Haar mesure on $\mathrm{GL}_{d}(F)$

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### Show a inequality in homogeneous Besov space

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### Span of parabolic inductions of discrete series representations

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### When can one bound the Hilbert transform on the torus in $L^1$?

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### Finding (and saturating) a sharp Babenko-Beckner inequality for finite fields

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### About definition of NTA domain

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### Wiener Corollary in “An introduction to harmonic analysis” by Yitzhak Katznelson

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### A question on a simple integral with a singular kernel?

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### Random Fourier series in Hilbert space

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### Find strictly subharmonic function that vanishes at infinity

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### Is there a nice orthogonal basis of spherical harmonics?

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### Pushforward of measures with Fourier decay

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### Dot product of functions on cosets

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### A question about super-harmonic functions

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### Reference requests: $W_{p}^1$-estimate for $(\triangle -\lambda)$ on Lipschitz domains

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### Does every compact abelian group contain a Kronecker set generating a dense subgroup?

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### Smoothing property of a certain singular integral operator of non-convolution type

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### Induced representations: space of continuous functions on $G$ to a Hilbert space

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### Integration by parts formula for the spectral fractional Laplacian

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### Using Fourier series to prove $-\int_0^1 u_{xxx}u_x \eta = \int_0^1 (u_{xx})^2\eta - \int_0^1 \frac{1}{2} (u_x)^2 \eta_{xx}$

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### Functions whose Fourier coefficients satisfy $ \sum_{k=1}^\infty |c_k| < 1 $?

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### Non-Hausdorff part of measure zero?

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### Mean value principle reversed

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### Twisted winding number

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### Sum of $\sin$ when angles shrink by $1/n$

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### Arbitrarily long compositions of a functions that stay within $[0,1]$

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### Harmonic analysis on reductive groups over $\mathbb{R}$

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### The Cauchy Transform, and the convergence of the Fourier-Stieltjes transforms of a sequence of measures

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### Integrability of $\exp\left(p\int_0^t |w(s,x(s,y))| \mathrm{d}s\right)$ for $w\in L^\infty(0,T;BMO(\mathbb{T}^d))$

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### Predual of $BMO(\mathbb{T}^d) $

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### A Frostman-type result for measures satisfying uniform lower density conditions

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### A simple oscillatory integral with a non-smooth phase

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### Beltrami equation with harmonic coefficient

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### Uncertainty principle, Sobolev embedding, and norm estimates

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