Questions tagged [spectral-theory]

Spectral theory is the study of generalized notions of eigenvalues and eigenvectors for linear operators in Banach spaces.

1,841 questions
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Spectral theorem on simple integral operator

Let $K(x): \mathbb R^d \to \mathbb R^d$, $K \in L^1(\mathbb R^d)$ such that $|K(x)| < M$ We define the integral operator $T$ as such: $\displaystyle(Tf)(x) = \int_{\mathbb R^d}f(y)K(|x-y|)dy$ ...
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Convergence in C* algebra forces spectra to approach limit point's spectrum

Let $A$ be a C* algebra with unity and let $x$ be a normal element and $(x_n)$ a sequence of normal elements converging to $x$. Also let $\Omega$ be a compact neighborhood of $\sigma(x)$. I am ...
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Estimates for pseudodifferential operator [on hold]

What is the difference between hypoelliptic estimate and subelliptic estimate? Thanks
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Book recommendation request on Spectral theory

Can someone please recommend to me a text that deals on spectral theory from the scratch covering the parts of a spectrum (approximate, point and compression) explicitly. Theorems and properties. ...
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Inverse of (i*I+A) for self adjoint operator

If we have that $A: H \rightarrow H$ is a bounded self-adjoint operator on a Hilbert space, then the spectrum of $A$ is entirely real, i.e. $\sigma(A) \subseteq \mathbb{R}$. Hence we know that $i$ is ...
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Why the space have to be complex in the spectral theorem for bounded self-adjoint operators?

In the spectral theorem for compact self-adjoint linear operators $T:H\to H$ (as stated in Conway's book), the Hilbert space $H$ can be real or complex. However, in the spectral theorem for bounded ...
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