#self-adjointness2 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 $ℌ={𝐿}^2(𝐵,d𝜇;ℂ)$. Local finiteness implies that...

mathsfunctional-analysisself-adjointnessnotesrough

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 $0\le 𝛼<1$. We say that an operator $𝐵$ defined on $𝐷(𝐴)$ is $𝐴$-bounded with relative bound $𝛼$ if...

mathsfunctional-analysisself-adjointnessnotesrough