1
vote
1answer
32 views

Blind deconvolution of a function convolved with itself

I have a function/vector $f$ that I know is the result of an unknown function $g$ convolved with itself: $f = g \ast g$ Is there any way to do a blind deconvolution on $f$ with this constraint?
0
votes
0answers
17 views

Integral of inverse function

On wikipedia and on the following mathstackexchange page, a formula for the sum of the integrals of a function and its inverse (with "corresponding" limits) is given, do you have a proper proof for ...
1
vote
0answers
89 views

Operator norm of the inverse

If I made no mistake, one can calculate the operator norm of the inverse of any given (invertible) operator $A: V\rightarrow V$ via: \begin{align}\|A^{-1}\| & = ...
1
vote
1answer
36 views

Exercise about linear operator

For $X$ Banach, I have to show that if $T\in\mathfrak{L}(X)$ and $||T||_{\mathfrak{L}(X)}<1$ then exists $(I-T)^{-1}$ and $$ (I-T)^{-1}=\sum_{n=0}^\infty T^n. $$ For the existence of $(I-T)^{-1}$ ...
0
votes
1answer
34 views

Inverse function without the original function

I am going through this paper, 'Certifiable Quantum Dice Or, True Random Number Generation Secure Against Quantum Adversaries' by Vazirani and Vidick. In 'Our results' section on the page 2, it says: ...
1
vote
1answer
224 views

Invertibility of a linear operator on a Hilbert space.

Let $H$ be an infinite dimensional Hilbert space over $\mathbb C$, $T$ be a continuous linear operator of $H$, $r(T)=\sup_{||x||=1}|(Tx|x)|$ be the numerical radius of $T$, and $z\in \mathbb C$, such ...
1
vote
1answer
215 views

Bounded operator inverse, norm and spectrum

I need help with an operator, I am not very good at functional analysis and need to find some properties of following operator: $X=C[(0,1)], A \in B(X); A[f(t)]=f(t^2)$ 1. I need to show that an ...
0
votes
1answer
49 views

If $A$ is invertible, so is $A^*A$

Let $A \in L(H)$, for a Hilbert space $H$. If $A$ is invertible, why is $A^*A$ invertible, too?
2
votes
3answers
135 views

Inverse of inverse of function?

What is the inverse of inverse of a function (I assume the original function is invertible)? Is this the original function? Is it always true?
1
vote
1answer
114 views

Inverse of trace class operator restricted to it's range

A paper I'm reading constructs the Cameron-Martin space in a way different than I'm used to, and in the process they gloss over a functional analysis result about the existence of an inverse. It ...
3
votes
1answer
111 views

For $T$ compact, $I-T$ left or right invertible implies $I-T$ invertible

Let $S\in B(X)$ be a bounded linear operator from $X$ onto $X$ and let $T\in K(X)$ be a compact linear operator from $X$ onto $X$. Then $$ S(I-T)=I \iff (I-T)S=I. $$ I don't know if we need the fact ...