Question

Spectral form of the operator $T:l^{2}\rightarrow l^{2}$ defined by $(\xi_{1},\xi_{2},\xi_{3},\ldots)\mapsto(\xi_{1}/1,\xi_{2}/2,\xi_{3}/3,\ldots)$

score 150 · Answer 1 · 2018-06-05 00:43:30

150

Views

Spectral form of the operator $T:l^{2}\rightarrow l^{2}$ defined by $(\xi_{1},\xi_{2},\xi_{3},\ldots)\mapsto(\xi_{1}/1,\xi_{2}/2,\xi_{3}/3,\ldots)$

Published on 05 Jun 2018 - 0:43

score 335 · Answer 2 · 2018-06-05 10:46:34

335

Views

What is the definition of generic surface in Buser's book: Geometry and spectra of compact Riemann surfaces?

Published on 05 Jun 2018 - 10:46

score 21 · Answer 3 · 2018-06-09 18:03:33

21

Views

For $A$ bounded operator, $\|A\|\ge |\alpha|$

Published on 09 Jun 2018 - 18:03

score 154 · Answer 4 · 2026-03-25 15:59:06

154

Views

Eigensystem of a linear interpolation operator. How to explain / interpret?

Published on 25 Mar 2026 - 15:59

score 122 · Answer 5 · 2018-06-11 04:07:22

122

Views

Theorem to rule out real (or imaginary) spectrum

Published on 11 Jun 2018 - 4:07

score 116 · Answer 6 · 2018-06-11 08:21:03

116

Views

Absolutely Continuous Spectrum of an operator $Af(x)=\sin x f(x)$

Published on 11 Jun 2018 - 8:21

score 306 · Answer 7 · 2018-06-13 09:45:14

306

Views

Conditions for the Validity of the "First Resolvent Identity" a.k.a. "Resolvent Equation"

Published on 13 Jun 2018 - 9:45

score 130 · Answer 8 · 2018-06-13 11:43:26

130

Views

Find spectrum of linear operator $T-I$ when you know eigenvalues of $T$

Published on 13 Jun 2018 - 11:43

score 46 · Answer 9 · 2018-06-13 12:01:06

46

Views

$m(u)=\sup\{a\in\mathbb{R}:u\geq a\text{ almost everywhere}\}$. Show that $\inf\{<M_uf,f>:||f||_2=1\}=m(u)$

Published on 13 Jun 2018 - 12:01

score 593 · Answer 10 · 2026-03-25 03:59:05

593

Views

Confusion about definition of continuous spectrum

Published on 25 Mar 2026 - 3:59

score 240 · Answer 11 · 2018-06-17 10:33:31

240

Views

Finding the set of eigenvalues and the spectrum of an operator

Published on 17 Jun 2018 - 10:33

score 341 · Answer 12 · 2018-06-18 15:21:49

341

Views

Basis formed by eigenvectors of compact normal operator on Hilbert space.

Published on 18 Jun 2018 - 15:21

score 119 · Answer 13 · 2026-03-21 22:21:29

119

Views

Find the spectrum σ(A).

Published on 21 Mar 2026 - 22:21

score 1.5k · Answer 14 · 2026-03-25 09:22:17

1.5k

Views

Does each compact operator have a non–zero eigenvector?

Published on 25 Mar 2026 - 9:22

score 554 · Answer 15 · 2018-06-22 16:05:05

554

Views

A question about the spectral theorem for unbounded self-adjoint operators

Published on 22 Jun 2018 - 16:05

List Question

Spectral form of the operator $T:l^{2}\rightarrow l^{2}$ defined by $(\xi_{1},\xi_{2},\xi_{3},\ldots)\mapsto(\xi_{1}/1,\xi_{2}/2,\xi_{3}/3,\ldots)$

What is the definition of generic surface in Buser's book: Geometry and spectra of compact Riemann surfaces?

For $A$ bounded operator, $\|A\|\ge |\alpha|$

Eigensystem of a linear interpolation operator. How to explain / interpret?

Theorem to rule out real (or imaginary) spectrum

Absolutely Continuous Spectrum of an operator $Af(x)=\sin x f(x)$

Conditions for the Validity of the "First Resolvent Identity" a.k.a. "Resolvent Equation"

Find spectrum of linear operator $T-I$ when you know eigenvalues of $T$

$m(u)=\sup\{a\in\mathbb{R}:u\geq a\text{ almost everywhere}\}$. Show that $\inf\{<M_uf,f>:||f||_2=1\}=m(u)$

Confusion about definition of continuous spectrum

Finding the set of eigenvalues and the spectrum of an operator

Basis formed by eigenvectors of compact normal operator on Hilbert space.

Find the spectrum σ(A).

Does each compact operator have a non–zero eigenvector?

A question about the spectral theorem for unbounded self-adjoint operators

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