I am wanting to cite the general Poisson summation formula for locally compact abelian groups (such as here). Does anyone know of a proper (preferably peer-reviewed) place where this is written down properly?
2026-02-23 06:55:01.1771829701
Citation for generalized poisson summation formula
74 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in NUMBER-THEORY
- Maximum number of guaranteed coins to get in a "30 coins in 3 boxes" puzzle
- Interesting number theoretical game
- Show that $(x,y,z)$ is a primitive Pythagorean triple then either $x$ or $y$ is divisible by $3$.
- About polynomial value being perfect power.
- Name of Theorem for Coloring of $\{1, \dots, n\}$
- Reciprocal-totient function, in term of the totient function?
- What is the smallest integer $N>2$, such that $x^5+y^5 = N$ has a rational solution?
- Integer from base 10 to base 2
- How do I show that any natural number of this expression is a natural linear combination?
- Counting the number of solutions of the congruence $x^k\equiv h$ (mod q)
Related Questions in FOURIER-ANALYSIS
- An estimate in the introduction of the Hilbert transform in Grafakos's Classical Fourier Analysis
- Verifying that translation by $h$ in time is the same as modulating by $-h$ in frequency (Fourier Analysis)
- How is $\int_{-T_0/2}^{+T_0/2} \delta(t) \cos(n\omega_0 t)dt=1$ and $\int_{-T_0/2}^{+T_0/2} \delta(t) \sin(n\omega_0 t)=0$?
- Understanding Book Proof that $[-2 \pi i x f(x)]^{\wedge}(\xi) = {d \over d\xi} \widehat{f}(\xi)$
- Proving the sharper form of the Lebesgue Differentiation Theorem
- Exercise $10$ of Chapter $4$ in Fourier Analysis by Stein & Shakarchi
- Show that a periodic function $f(t)$ with period $T$ can be written as $ f(t) = f_T (t) \star \frac{1}{T} \text{comb}\bigg(\frac{t}{T}\bigg) $
- Taking the Discrete Inverse Fourier Transform of a Continuous Forward Transform
- Is $x(t) = \sin(3t) + \cos\left({2\over3}t\right) + \cos(\pi t)$ periodic?
- Translation of the work of Gauss where the fast Fourier transform algorithm first appeared
Related Questions in HARMONIC-ANALYSIS
- An estimate in the introduction of the Hilbert transform in Grafakos's Classical Fourier Analysis
- Show that $x\longmapsto \int_{\mathbb R^n}\frac{f(y)}{|x-y|^{n-\alpha }}dy$ is integrable.
- Verifying that translation by $h$ in time is the same as modulating by $-h$ in frequency (Fourier Analysis)
- Seeking an example of Schwartz function $f$ such that $ \int_{\bf R}\left|\frac{f(x-y)}{y}\right|\ dy=\infty$
- Computing Pontryagin Duals
- Understanding Book Proof that $[-2 \pi i x f(x)]^{\wedge}(\xi) = {d \over d\xi} \widehat{f}(\xi)$
- Expanding $\left| [\widehat{f}( \xi + h) - \widehat{f}( \xi)]/h - [- 2 \pi i f(x)]^{\wedge}(\xi) \right|$ into one integral
- When does $\lim_{n\to\infty}f(x+\frac{1}{n})=f(x)$ a.e. fail
- The linear partial differential operator with constant coefficient has no solution
- Show $\widehat{\mathbb{Z}}$ is isomorphic to $S^1$
Related Questions in LOCALLY-COMPACT-GROUPS
- Locally Compact Hausdorff Topologial Group but not Sequential?
- existence of weak* continuous means for amenable locally compact groups
- Decomposition of $L^2(S^1)$
- How can I prove that $\bigcap\limits_{n=0}^{+\infty} \Gamma_{j,n}=\emptyset$?
- Integral converges "$UZg$ is closed in $G$"
- A small problem on the annihilators of some subgroups
- Samuel compactification of the real line
- Every quasicharacter of an open subgroup extends to a quasicharacter of the group
- The measurability of convolution in locally compact group
- Convolution of a function and a measure.
Related Questions in POISSON-SUMMATION-FORMULA
- Understanding Proof of Poisson Summation Formula
- Evaluating $\displaystyle\int_{-\infty+iy}^{\infty+iy}(cv)^{-k}e\left(\frac{-m}{c^2v}-nv\right)dv$.
- Probability density of the fractional part of |σZ| as σ→∞?
- Minkowski's Theorem by Harmonic Analysis
- G(k,X) is a modular form of weight k and character X
- Proving the Partial Fraction Decomposition of the Hyperbolic Cotangent Function by using Poisson Summation
- Proving the relation: $\sum_{n\in\Bbb Z} \frac{2a}{a^2+4 \pi^2 n^2} = \sum_{n\in\Bbb Z} e^{-a \left\lvert n \right\rvert}$
- Evaluation of a sum by means of Poisson sum formula and digamma function
- Confusion about applying Poisson's Sum Formula
- Question on Poisson summation formula and Fourier transform
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- 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?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- 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
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?