Are there any functions that are their own Fourier transforms other than $e^{-\pi x^2} $?
2025-01-12 23:58:32.1736726312
Fourier transform invariant functions other than the bell curve?
149 Views Asked by user47376 https://math.techqa.club/user/user47376/detail At
1
There are 1 best solutions below
Related Questions in FOURIER-ANALYSIS
- The distribution of fourier coefficients of a Rademacher sequence
- Effect of sampling frequency on Discrete Fourier Transform?
- Fourier transform to determine stability of fixpoint of equation with temporal convolution
- Find Fourier transform of triangular function based on a Fourier results of rectangular
- Let $f\in C^1[-\pi ,\pi]$ be such that $f(-\pi)=f(\pi)$Show that $\{na_n\} $ is convergent to $0$
- Is this Fourier Transform relation correct?
- What are all functions of the form $\frac{\cosh(\alpha x)}{\cosh x+c}$ self-reciprocal under Fourier transform?
- Use the Inverse Fourier transform to show the Dirac-Delta function as a limit of the sinc function
- Compute Fourier Transform using conditional expectation
- A question involving sharpening the bound on Sobolev type inequality with Sobolev spaces in terms of distributions of Schwartz functions
Related Questions in NORMAL-DISTRIBUTION
- Multi sample chi-square distribution
- Distribution of $Y$ derived from standard normal
- Find expectation of Z (normal)
- Bayesian Gaussian Mixture model
- Distribution of $Y= \frac{X_1}{|X_2|}$?
- How can I solve the probability of a sample mean exceeds population mean if I'm not provided means?
- What is the proportion of the population listed below is highly advanced (greater than or equal to 145?)
- Cumulative distribution function of function of normal random variables
- Expectation of the inverse of a shifted squared of a normal random variable!
- Finding parameters of normal distribution
Related Questions in FOURIER-SERIES
- Why is this true for this Fourier series $exp(ax)$ $x\in(0,\pi)$
- Interpreting function notation?
- Asymptotic expansion for the solution of linear KDV eq.
- Effect of sampling frequency on Discrete Fourier Transform?
- How can I calculate $\int_{-\pi}^{\pi} \cos^6(x)dx$ by using Parseval's theorem
- Let $f\in C^1[-\pi ,\pi]$ be such that $f(-\pi)=f(\pi)$Show that $\{na_n\} $ is convergent to $0$
- Proof of Properties of Fourier series in CT
- Derivative of series
- Some properties of the homogeneous spaces on $\mathbb{T}$
- Fourier series, infinite series
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Refuting the Anti-Cantor Cranks
- Find $E[XY|Y+Z=1 ]$
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- What are the Implications of having VΩ as a model for a theory?
- How do we know that the number $1$ is not equal to the number $-1$?
- Defining a Galois Field based on primitive element versus polynomial?
- Is computer science a branch of mathematics?
- Can't find the relationship between two columns of numbers. Please Help
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- A community project: prove (or disprove) that $\sum_{n\geq 1}\frac{\sin(2^n)}{n}$ is convergent
- Alternative way of expressing a quantied statement with "Some"
Popular # Hahtags
real-analysis
calculus
linear-algebra
probability
abstract-algebra
integration
sequences-and-series
combinatorics
general-topology
matrices
functional-analysis
complex-analysis
geometry
group-theory
algebra-precalculus
probability-theory
ordinary-differential-equations
limits
analysis
number-theory
measure-theory
elementary-number-theory
statistics
multivariable-calculus
functions
derivatives
discrete-mathematics
differential-geometry
inequality
trigonometry
Popular Questions
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- How to find mean and median from histogram
- Difference between "≈", "≃", and "≅"
- Easy way of memorizing values of sine, cosine, and tangent
- How to calculate the intersection of two planes?
- What does "∈" mean?
- If you roll a fair six sided die twice, what's the probability that you get the same number both times?
- Probability of getting exactly 2 heads in 3 coins tossed with order not important?
- Fourier transform for dummies
- Limit of $(1+ x/n)^n$ when $n$ tends to infinity
There is a complete characterization of the probability densities that are (modulo a constant factor) their own Fourier transforms (aka characteristic functions) in a paper of K. Schladitz and H.J. Engelbert: "On probability density functions which are their own characteristic functions", Theory Probab. Appl., vol. 40 (1995) pp. 577–581. The class is surprisingly large.