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 153 · Answer 1 · 2026-04-17 08:22:38

153

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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 17 Apr 2026 - 8:22

score 339 · Answer 2 · 2026-05-11 01:11:12

339

Views

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

Published on 11 May 2026 - 1:11

score 24 · Answer 3 · 2026-04-12 02:04:52

24

Views

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

Published on 12 Apr 2026 - 2:04

score 157 · Answer 4 · 2026-05-11 00:24:20

157

Views

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

Published on 11 May 2026 - 0:24

score 125 · Answer 5 · 2026-04-15 12:38:18

125

Views

Theorem to rule out real (or imaginary) spectrum

Published on 15 Apr 2026 - 12:38

score 119 · Answer 6 · 2026-04-14 15:11:03

119

Views

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

Published on 14 Apr 2026 - 15:11

score 309 · Answer 7 · 2026-04-12 14:44:41

309

Views

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

Published on 12 Apr 2026 - 14:44

score 133 · Answer 8 · 2026-04-14 22:36:11

133

Views

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

Published on 14 Apr 2026 - 22:36

score 49 · Answer 9 · 2026-04-16 19:46:46

49

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 16 Apr 2026 - 19:46

score 599 · Answer 10 · 2026-05-04 04:14:55

599

Views

Confusion about definition of continuous spectrum

Published on 04 May 2026 - 4:14

score 243 · Answer 11 · 2026-04-10 13:15:44

243

Views

Finding the set of eigenvalues and the spectrum of an operator

Published on 10 Apr 2026 - 13:15

score 344 · Answer 12 · 2026-04-12 16:51:33

344

Views

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

Published on 12 Apr 2026 - 16:51

score 124 · Answer 13 · 2026-05-10 15:19:19

124

Views

Find the spectrum σ(A).

Published on 10 May 2026 - 15:19

score 1.5k · Answer 14 · 2026-05-10 18:57:18

1.5k

Views

Does each compact operator have a non–zero eigenvector?

Published on 10 May 2026 - 18:57

score 557 · Answer 15 · 2026-04-11 08:31:34

557

Views

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

Published on 11 Apr 2026 - 8:31

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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