El programa y el horario de los dos cursos

El aula: 420 del Módulo 17 de la Fac. de Ciencias, UAM

Curso I. Towards a numerization of the Gelfand theory

Los miércoles 1, 8, 15 y 22 de octubre, de 14:30 a 15:30

1) Why there exists no constructive proof to Wiener's 1/f theorem?

2) Invisible spectrum and critical constants of an algebra

3) A corona theorem for H^infty trace algebras

4) Invisible spectrum of Fourier multipliers under the Muckenhoupt condition

References

1. N.Wiener and H.R.Pitt, On absolutely convergent Fourier-Stieltjes

transforms, Duke Math. J., 4:2 (1938), 420-436.

2. N.Nikolski, In search for the invisible spectrum, Ann. Inst.

Fourier, 49:6 (1999), 1925-1998.

3. P.Gorkin, R.Mortini, N.Nikolski, Norm controlled inversions and a

corona theorem for H∞-quotient algebras, J. Funct. Anal. 255 (2008),

no. 4, 854–876.

4. N.Nikolski and I.Verbitsky, Fourier multipliers for weighted L2

spaces with Lévy-Khinchin-Schoenberg weights, arXiv:1404.4380v1 (2014).

Curso II. Sublinear dimension growth in the KMT (Kreiss Matrix Theorem)

Los jueves 2, 9, 16 y 23 de octubre, de 14:30 a 15:30

1) The KMT and stable Runge-Kutta approximations

2) Bernstein-type inequalities for rational functions

3) Basis and unconditional basis constants (following McCarthy-Schwartz)

4) Sublinear dimension growth in the KMT.

References

1. M.N.Spijker, Numerical stability, stability estimates and related

conditions in the numerical solution of initial value problems,

Lecture Notes Leiden, 1998; http://www.math.leidenuniv.nl/spijker/

2. C.A.McCarthe and J.T.Schwartz, On the norm of a finite Boolean

algebra of projections, and applications to theorems of Kreiss and

Morton, Comm. Pure Appl. Math., 18 (1965), 191-201.

3. N.Nikolski, Sublinear dimension growth in the Kreiss matrix

theorem, Algebra i Analiz 25 (2013), no. 3, 3-51; reprinted in: St.

Petersburg Math. J. 25 (2014), no. 3, 361–396.