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Spectral and pseudospectral functions of various dimensions for symmetric systems
| Content Provider | Semantic Scholar |
|---|---|
| Author | Mogilevskii, Vadim |
| Copyright Year | 2016 |
| Abstract | The main object of the paper is a symmetric system Jy′ − B(t)y = ⋋∆(t)y defined on an interval Ι = [a, b) with the regular endpoint a. Let φ(⋅, λ) be a matrix solution φ(⋅, λ) of this system of an arbitrary dimension, and let Vfs=∫Iφ∗tsΔtftdt$$ \left( V\kern0.5em f\right)(s)={\displaystyle \underset{I}{\int }{\varphi}^{\ast}\left( t, s\right)\varDelta (t) f(t) d t} $$ be the Fourier transform of the function f(⋅) ∈ LΔ2(I). We define a pseudospectral function of the system as a matrix-valued distribution function σ(·) of the dimension nσ such that V is a partial isometry from LΔ2ItoL2σ;ℂnσ$$ {L}_{\varDelta}^2(I)\kern0.5em \mathrm{t}\mathrm{o}\kern0.5em {L}^2\left(\sigma; \kern0.5em {\mathbb{C}}^{n_{\sigma}}\right) $$ with minimally possible kernel. Moreover, we find the minimally possible value of nσ and parametrize all spectral and pseudospectral functions of every possible dimensions nσ by means of a Nevanlinna boundary parameter. The obtained results develop the results by Arov and Dym; Sakhnovich, Sakhnovich and Roitberg; Langer and Textorius. |
| Starting Page | 679 |
| Ending Page | 711 |
| Page Count | 33 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s10958-017-3259-x |
| Volume Number | 221 |
| Alternate Webpage(s) | https://arxiv.org/pdf/1611.03174v1.pdf |
| Alternate Webpage(s) | https://doi.org/10.1007/s10958-017-3259-x |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
