# Questions tagged [fourier-analysis]

The representation of functions (or objects which are in some generalize the notion of function) as constant linear combinations of sines and cosines at integer multiples of a given frequency, as Fourier transforms or as Fourier integrals.

**2**

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### Zygmund class, Schwartz class and Littlewood-Paley projection operators

**2**

**1**answer

### Estimate of Hölder Norms (Littlewood–Paley theory)

**3**

**2**answers

### Vanishing convolution between density and compactly supported function

**11**

**1**answer

### Does there exist an upper bound on the Fourier coefficients of the reciprocal theta function $\frac {1}{\theta}$?

**0**

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### Inverse of a Function Using its Fourier Series

**4**

**1**answer

### Scaling of double convolution

**3**

**1**answer

### A convolution type singular integral operator with log

**3**

**2**answers

### What is the distribution of the following limit?

**2**

**2**answers

### Decay estimate of Fourier transform of a compactly supported function

**2**

**0**answers

### Half-integer Fourier transform

**0**

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### Hamiltonian of Benjamin-Ono equation

**5**

**1**answer

### Schwartz regularity for the density of a stochastic process

**5**

**1**answer

### Generalization of Bernstein’s inequality

**2**

**1**answer

### Uniform convergence of Eigenfunction decomposition on Riemannian sphere?

**2**

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

**6**

**1**answer

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

**0**

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### Can I write this series in a recursive way?

**3**

**2**answers

### Fourier transform of eigenvalue distribution of GUE matrices

**6**

**0**answers

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

**2**

**1**answer

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

**2**

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### Definition of a continuous Gabor frame

**0**

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### Magnitude spectrum of a cascade of filter

**3**

**1**answer

### What corresponds to the operation of taking traces in of the Fourier transformation on a finite group?

**3**

**1**answer

### “Reversed” Bernstein Inequality

**1**

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### Decay conditions on the Fourier coefficients ensuring that a smooth function doesn't vanish on some interval

**-1**

**1**answer

### What does $O(N)$ mean in this article and how does it imply this lemma?

**1**

**1**answer

### Integrability of fractional heat kernel

**2**

**0**answers

### What are the necessary/sufficient conditions for a Fourier transform to have at least $k$ roots?

**4**

**1**answer

### Vanishing of the product of a function and its own Fourier transform

**1**

**0**answers

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

**4**

**1**answer

### Smallest regular $m$-gon covering a regular $n$-gon

**0**

**1**answer

### Variance of spectral density is related to the gradient of signal?

**1**

**1**answer

### Does Bochner's Theorem apply to Fourier coefficients?

**6**

**1**answer

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

**0**

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### Context for this discrete Cauchy integral formula

**1**

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### Function of several variables whose hessian is a Hankel matrix

**1**

**1**answer

### How many Fourier coefficients of a sparse signal $f=\sum_{n=1}^Nc_n\delta_{t_n}$ are needed to determine $f$ uniquely?

**0**

**0**answers

### Some density properties about Sobolev periodic spaces

**7**

**1**answer

### What makes Gaussian distributions special? Local field version?

**5**

**0**answers

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

**7**

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

**1**

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### Factoring a complex function such that it is analytic in upper and lower plane

**0**

**1**answer

### Can a Fourier transform be performed on irregularly sampled data with timestamps?

**1**

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### Second question on a real sequence

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### Deriving periodical processes from a finite time series

**1**

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### Converse to Hausdorff-Young (or Riesz-Thorin) for finite cyclic groups?

**1**

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

**3**

**1**answer

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

**2**

**0**answers

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

**1**

**1**answer