N. Azamov

activity

20072022

most citedThe spectral shift function and spectral flow

26 citations · 80 across the 28 of their papers we have counts for

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17 papers · 1 filter

math.SP2021

Limiting absorption principle and singular spectrum

Nurulla Azamov

In this paper I give an explicit construction of an analogue of eigenspace for points of the singular spectrum of a self-adjoint operator. This construction is based on an abstract…

math.SP2021

Coupling Resonances and Spectral Properties of the Product of Resolvent and Perturbation

Nurulla Azamov, Tom Daniels

Given a self-adjoint operator $H_{0}$ and a relatively compact self-adjoint perturbation $V$ , we study in some detail the spectral properties of the product $(H_{0} - z)^{- 1} V$ . For some…

math.SP2021

Relative stability of singular spectrum

Nurulla Azamov

There are classical theorems of analysis which, given certain conditions on a perturbation, assert stability of the essential and absolutely continuous components of the spectrum o…

math.SP2021

Spectral flow inside essential spectrum V: on absorbing points of coupling resonances

Nurulla Azamov

Let $H_{0}$ and $V$ be self-adjoint operators, such that $V$ admits a factorisation $V = F^{*} J F$ with bounded self-adjoint $J$ and $∣ H_{0} ∣^{1/2}$ -compact $F .$ Coupling resonance functi…

math.SP2021★ 1 cited

Spectral flow inside essential spectrum III: coupling resonances near essential spectrum

Nurulla Azamov

Given a self-adjoint operator $H_{0}$ and a relatively $H_{0}$ -compact self-adjoint operator $V,$ the functions $r_{j} (z) = - σ_{j}^{- 1} (z),$ where $σ_{j} (z)$ are eigenvalues of the compact…

math.SP2021

Spectral flow inside essential spectrum II: resonance set and its structure

Nurulla Azamov

This paper is a continuation of the study of spectral flow inside essential spectrum initiated in \cite{AzSFIES}. Given a point $λ$ outside the essential spectrum of a self-adjoint…