I'm trying to solve the following distribution equation for $T$: $$ xT'=1 $$ I know that the distribution pv$\frac{1}{x}$ satisfies $x$pv$\frac{1}{x}=1$ but i don't really know what to do from there, how do i go about finding the "primitive" of pv$\frac{1}{x}$ to solve for $T$ from this?. Sorry if this is obvious but I'm very new to studying distribution theory so any help is appreciated.
2026-03-26 14:42:23.1774536143
Primitive of Cauchy Principal Value?
44 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in DISTRIBUTION-THEORY
- $\lim_{n\to\infty}n^2(\int_{-1/n}^0u(x-s)ds -\int_0^{1/n}u(x-s)ds)$ where $u(x)$ an infinitely differentiable function on R
- Approximating derivative of Dirac delta function using mollifiers
- Distributional solution of differential equation
- Solution of partiell differential equation using the fundamental solution
- Find a sequence converging in distribution but not weakly
- How to prove this Dirac delta limit representation is correct?
- Properties about Dirac Delta derivative
- Does $\mathrm{e}^x$ belong to $\mathcal{S}'(\mathbb{R}^n)$?
- Is there a sense in which this limit is zero?
- Schwartz kernel theorem and dual topologies
Related Questions in CAUCHY-PRINCIPAL-VALUE
- Reducing this principal value integral to something I can evaluate numerically
- Bose-Einstein function as real part of polylogarithm: $\overline{G}_{s}(x)= \Re \mathrm{Li}_{s+1}(e^x)$
- Cauchy Principal Value and Divergent Integrals
- What does the principal value $\mathscr{P}$ mean exactly in this integral?
- Asymptotics of an integral $\mathscr{P} \int_{0}^{\infty} \frac{d\omega}{e^{\omega} - 1} \frac{\omega}{\omega^{2} - x^{2}}$ involving principal value
- Help understanding the weak topology on the dual of the Schwartz space?
- Evaluation of $\int_{-\infty}^{\infty} \frac{\sin(x)}{x^n} \,\mathrm{d}x $?
- How to Calculate PV$\int_0^{\infty}\frac{\cos ax}{x^4-1}\:dx\: $for all a in R
- Principal value of 1/x
- Principale value of complex integral
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?