English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this work, we focus on the multiplicity of singular spectrum for operatorsof the form $A^\omega=A+\sum_{n}\omega_n C_n$ on a separable Hilbert space$\mathcal{H}$, for a self-adjoint operator $A$ and a countable collection$\{C_n\}_{n}$ of non-negative finite rank operators. When $\{\omega_n\}_n$ areindependent real random variables with absolutely continuous distributions, weshow that the multiplicity of singular spectrum is almost surely bounded aboveby the maximum algebraic multiplicity of eigenvalues of$\sqrt{C_n}(A^\omega-z)^{-1}\sqrt{C_n}$ for all $n$ and almost all$(z,\omega)$. The result is optimal in the sense that there are operators wherethe bound is achieved. Using this, we also provide effective bounds onmultiplicity of singular spectrum for some special cases.

Multiplicity theorem of singular Spectrum for general Anderson type Hamiltonian