Naslov
On quasi-definite quadratic forms in a Hilbert space and applications

Autori
Grubišić, Luka ; Kostrykin, Vadim ; Makarov, Konstantin A. ; Veselić, Krešimir

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
80th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) / - , 2009

Skup
80th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)

Mjesto i datum
Gdańsk, Poljska, 09.02.2009. - 13.02.2009

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
indefinite quadratic forms; representation theorems

Sažetak
We present a perturbation theory for sign-indefinite, not necessarily semi-bounded, quadratic forms in a Hilbert space. As a first step, and under an additional qualitative assumption on the algebraic structure of the form, we prove an operator representation theorem. This structural restriction is in analogy to the structure of the so called quasi-definite matrices from Linear Algebra. As prototype applications for our perturbation results we consider consequences for the theory of systems of partial differential equations. More to the point, we obtain several subspace perturbation theorems for these “quasi-definite operators”. The results are obtained using weakly formulated Riccati and Sylvester operator equations. Accompanying estimates on the perturbation of the spectra are also presented. Various estimation approaches are compared on the explicit example of the Stokes block matrix operator. This operator is associated to the Cosserat eigenvalue problem. We also show that on this example some of our estimates can be attained. The present work continues previous studies of weakly formulated operator equations from L. Grubišić and K. Veselić. On weakly formulated Sylvester equation and applications. Integral Equations and Operator Theory, 58(2), 2007. This is a joint work with Vadim Kostrykin, Konstantin Makarov and Krešimir Veselić.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA