Contents/conteúdo

Mathematics Department Técnico Técnico

Operator Theory, Complex Analysis and Applications Seminar  RSS

Sessions

06/12/2012, 16:30 — 17:30 — Room P4.35, Mathematics Building
Cristina Diogo, ISCTE-IUL and CAMGSD

Corona conditions and symbols with a gap around zero

Convolution equations on a finite interval (which we can assume to be [0,1 ]) lead to the problem of factorizing matrix functions G=[e 1 0 g e 1 ] where e θ(ξ)=e iθξ, θ and gL (). Here we consider g of the form g=a +e μ+a e σ with a ±H ( ±) and μ,σ>0 . Imposing some corona-type conditions on a ±, we show that solutions to the Riemann-Hilbert problem Gh +=h , with h ±(H ( ±)) 2 , can be determined explicitly and conditions for invertibility of the Toeplitz operator with symbol G in (H p +) 2 can be derived from them.

Seminar organized in the context of the project PTDC/MAT/121837/2010.

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