Ricardo Vidal Joint talk with Vaja Tarieladze (Georgian Academy of Sciences)

Strong minimality of Gaussian integrals

Abstract: Let E be a be a finite-dimensional Hilbert space with dim(E) ≥ 1, U(E) be the set of all isometric linear operators u : E → E and γ be the standard Gaussian measure on E. We will discuss some applications of the next statement which expresses ”the strong minimality” of the Gaussian integrals. Proposition. Let μ be a positive measure (not necessarily finite) given on the Borel σ-algebra of E such that

∫_{E} ∥x∥^{2}dμ(x) = 1.

Then for any positively 2-homogeneous Borel measurable function f : E → C with f(0) = 0, we have:

∫_{E} |f(x)|dγ(x) ≤ dim(E) sup_{u∈U(E)} ∫_{E} |f(ux)|dμ(x)

holds. This talk is based on [TV].

REFERENCES

[TV] Tarieladze V., Vidal, R. Strong minimality of Gaussian summing norm, Acta Mathematica Vietnamica, Vol. 28, Number 2, 2003, pp. 225-240.

AUTHORS

Ricardo Vidal

Departamento de Matematica Aplicada,I E. T. S. E. de Telecomunicacion, Universidad de Vigo, Vigo, Spain. E-mail: rvidal@dma.uvigo.es

Vaja Tarieladze Muskhelishvili Institute of Computational Mathematics, Georgian Academy of Sciences, Tbilisi–93, Georgia. E-mails: tar@gw.acnet.ge visit01@dma.uvigo.es