What is the total variation of a dirac delta function $\delta(x)$? My guess is that it is something like $\infty$. If not defined, what would be the best way to define?
2026-03-26 17:31:44.1774546304
What is the total variation of a dirac delta function $\delta(x)$?
1.3k Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in REAL-ANALYSIS
- how is my proof on equinumerous sets
- Finding radius of convergence $\sum _{n=0}^{}(2+(-1)^n)^nz^n$
- Optimization - If the sum of objective functions are similar, will sum of argmax's be similar
- On sufficient condition for pre-compactness "in measure"(i.e. in Young measure space)
- Justify an approximation of $\sum_{n=1}^\infty G_n/\binom{\frac{n}{2}+\frac{1}{2}}{\frac{n}{2}}$, where $G_n$ denotes the Gregory coefficients
- Calculating the radius of convergence for $\sum _{n=1}^{\infty}\frac{\left(\sqrt{ n^2+n}-\sqrt{n^2+1}\right)^n}{n^2}z^n$
- Is this relating to continuous functions conjecture correct?
- What are the functions satisfying $f\left(2\sum_{i=0}^{\infty}\frac{a_i}{3^i}\right)=\sum_{i=0}^{\infty}\frac{a_i}{2^i}$
- Absolutely continuous functions are dense in $L^1$
- A particular exercise on convergence of recursive sequence
Related Questions in DEFINITION
- How are these definitions of continuous relations equivalent?
- If a set is open, does it mean that every point is an interior point?
- What does $a^b$ mean in the definition of a cartesian closed category?
- $\lim_{n\to \infty}\sum_{j=0}^{[n/2]} \frac{1}{n} f\left( \frac{j}{n}\right)$
- Definition of "Normal topological space"
- How to verify $(a,b) = (c,d) \implies a = c \wedge b = d$ naively
- Why wolfram alpha assumed $ x>0$ as a domain of definition for $x^x $?
- Showing $x = x' \implies f(x) = f(x')$
- Inferior limit when t decreases to 0
- Is Hilbert space a Normed Space or a Inner Product Space? Or it have to be both at the same time?
Related Questions in DIRAC-DELTA
- What is the result of $x(at) * δ(t-k)$
- Solution to ODE with Dirac Delta satisfies ODE
- How is $\int_{-T_0/2}^{+T_0/2} \delta(t) \cos(n\omega_0 t)dt=1$ and $\int_{-T_0/2}^{+T_0/2} \delta(t) \sin(n\omega_0 t)=0$?
- Approximating derivative of Dirac delta function using mollifiers
- How to prove this Dirac delta limit representation is correct?
- $\int_{-\epsilon}^\epsilon\delta(f(x))g(x)dx=\frac{g(0)}{f'(0)}$?
- Properties about Dirac Delta derivative
- Dirac / Fourier relation
- Prove that $\frac{1}{\epsilon}\int_{\mathbb{R}}f(t).\exp\left(\frac{-\pi(x-t)^2}{\epsilon^2}\right)dt \xrightarrow{\epsilon \to 0}f(x) $
- Integral involving delta functions and vector quantities
Related Questions in BOUNDED-VARIATION
- Method for evaluating Darboux integrals by a sequence of partitions?
- Function of bounded variation which is differentiable except on countable set
- Variation with respect to the projective tensor norm of a matrix of bounded variation functions
- Associativity of an integral against a function with finite variation
- Suppose $f(x)$ is of bounded variation. Show $F(x) = \frac{1}{x} \int_0^x f(t) \, dt$ is also of bounded variation.
- Is there a sufficient condition for which derivative of $\sum_{n=0}^{\infty} a_n x^n$ is bounded for all $x \in \mathbb{R}$?
- Looking for the name of this property, if it has one.
- Bounded Variation Proof
- Rearranging a sequence of bounded variation
- If $f$ is $g$-Riemann-Stieltjes integrable on $[a,b]$, prove that it's $g$-RS-integrable on $[a,c] \subset [a,b]$
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?