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.

**3**

**0**answers

### On smoothness of a function and decay of its Fourier transform

**1**

**1**answer

### Functions belong to $L^{\frac{2n}{n+1}}$ whose Fourier transforms are infinite on $S^{n-1}$

**1**

**0**answers

### Is the ratio of two distinct zeros of a Bessel function of the first kind an irrational number?

**-2**

**1**answer

### Relationship between “Radial” Fourier transform and Fourier transform, especially at infinity

**3**

**0**answers

### Multi-parameter stationary phase asymptotic expansion

**5**

**0**answers

### Extremal polynomial majorants of $\log{|f|}$: a multivariate extension of a theorem of Carneiro and Vaaler

**3**

**1**answer

### Detecting if a series represents a rational function

**0**

**1**answer

### Uniqueness of solution to system of integral equations

**0**

**0**answers

### Initial value theorem for Fourier transform

**1**

**2**answers

### Fourier transform of a generalized function on the plane

**5**

**0**answers

### Convolution theorem on a non-abelian Lie group

**11**

**1**answer

### Nonlinear Schrödinger equation with discrete Laplacian

**1**

**0**answers

### Calculus of variation with discontinuous solutions?

**7**

**2**answers

### Characterizing pseudo-differential operators as a subalgebra of continuous endomorphisms of tempered distributions

**0**

**1**answer

### The minimum of the maximum of a sequence of sinc functions

**2**

**0**answers

### Star-convex curve and Fourier series

**1**

**0**answers

### Conditions for Poisson summation (for discontinuous functions)

**13**

**1**answer

### A question on the sine function

**4**

**1**answer

### $L^1$ norm of Littlewood polynomials on the unit circle

**10**

**0**answers

### A combinatorial proof of the Harrow--Kolla--Schulman theorem

**11**

**1**answer

### Is there a physical/geometric proof for L^2 boundedness of Bourgain's maximal function along the squares?

**2**

**0**answers

### Theory of distributions on various domains

**6**

**1**answer

### graph signal processing

**2**

**1**answer

### Are the Prolate Spheroidal Wave Functions absolutely integrable?

**2**

**0**answers

### Average of irrational flow on the torus

**2**

**1**answer

### Can we say that the Riemann zeta zero spectrum backbone asymptotic is $\frac{H_{\text{n}}+\frac{\partial \vartheta (t)}{\partial t}}{t}$?

**3**

**0**answers

### A uniform Riemann sum approximation of the integral of the Fejer kernels

**1**

**0**answers

### Discrete Wavelet Transform and Gaussian decay

**0**

**0**answers

### Composing functions whose derivatives have $L^1$ Fourier transforms

**2**

**1**answer

### About the Fourier transform of the logarithm function

**2**

**0**answers

### A specific Schwartz function $f$ on $\mathbb C^2$

**6**

**1**answer

### $L^p$ estimates and functions with positive Fourier transform

**1**

**1**answer

### Which Fourier transform is the correct one?

**0**

**0**answers

### Positivity of an integral with product of functions and their Fourier transforms

**1**

**0**answers

### On the bound of the Stein-Wainger oscillatory integral

**4**

**0**answers

### Is there a Lie group Fourier transform for D-modules?

**1**

**0**answers

### Functional equation with Fourier transform

**3**

**2**answers

### Decay of bandlimited function

**0**

**0**answers

### Positive Convolution Root

**1**

**0**answers

### Comparison of (square) of a function and its Fourier transform in an integral

**-2**

**1**answer

### A question on the zeros involving the equation containing exponential factor [closed]

**2**

**0**answers

### Existence of unbounded $M \subset \Bbb{R}$ of finite measure s.t. $1_M$ is $L^p$-Fourier multiplier

**0**

**0**answers

### Can we deduce the sign of this integral which includes cosine transform?

**15**

**3**answers

### Is there an “analytical” version of Tao's uncertainty principle?

**0**

**0**answers

### Solution of a functional equation with cosine transform

**2**

**1**answer

### Solving classical parabolic equation by using Littlewood-Paley theory

**3**

**0**answers

### Reverse Markov-Bernstein inequality for trigonometric polynomials

**4**

**0**answers

### Is there a categorical foundation for manifolds of bounded geometry and bandlimited functions?

**0**

**0**answers

### Is the product of two Sobolev functions in L^p?

**3**

**0**answers