#self-adjointness

2 posts

May 19, 2026

Notes on Lewin Ch4: Spectral Theorem and Functional Calculus

1 Multiplication Operators Let $𝐵 \subset ℝ^{𝑑}$ be Borel, and let $𝜇$ be a locally finite Borel measure on $𝐵$ . We set $ℌ = 𝐿^{2} (𝐵, d 𝜇; ℂ)$ . Local finiteness implies that...

maths functional-analysis self-adjointness notes rough

May 15, 2026

Notes on Lewin Ch3: Self-adjointness Criteria: Rellich, Kato and Friedrichs

Rellich–Kato Let $(𝐴, 𝐷 (𝐴))$ be a self-adjoint operator and $0 \leq 𝛼 < 1$ . We say that an operator $𝐵$ defined on $𝐷 (𝐴)$ is $𝐴$ -bounded with relative bound $𝛼$ if...

maths functional-analysis self-adjointness notes rough