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1. On Littlewood"s constants

Beliaev, Dmitri

et al.

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).

Smirnov, Stanislav

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).

On Littlewood"s constants2005In: Bulletin of the London Mathematical Society, ISSN 0024-6093, E-ISSN 1469-2120, Vol. 37, p. 719-726Article in journal (Refereed)

Abstract [en]

In two papers, Littlewood studied seemingly unrelated constants: (i) the best alpha such that for any polynomial f, of degree n, the areal integral of its spherical derivative is at most const -n(alpha), and (ii) the extremal growth rate beta of the length of Green's equipotentials for simply connected domains. These two constants are shown to coincide, thus greatly improving known estimates on a.

We prove orthogonality and compute explicitly the (quadratic) norms for super-Jack polynomials SP lambda((z1, horizontal ellipsis ,zn),(w1, horizontal ellipsis ,wm);theta) with respect to a natural positive semi-definite, but degenerate, Hermitian product ⟨center dot,center dot⟩n,m,theta '. In case m=0 (or n=0), our product reduces to Macdonald's well-known inner product ⟨center dot,center dot⟩n,theta ', and we recover his corresponding orthogonality results for the Jack polynomials P lambda((z1, horizontal ellipsis ,zn);theta). From our main results, we readily infer that the kernel of ⟨center dot,center dot⟩n,m,theta ' is spanned by the super-Jack polynomials indexed by a partition lambda not containing the mxn rectangle (mn). As an application, we provide a Hilbert space interpretation of the deformed trigonometric Calogero-Moser-Sutherland operators of type A(n-1,m-1).

A factoring theorem for the Bergman space1994In: Bulletin of the London Mathematical Society, ISSN 0024-6093, E-ISSN 1469-2120, Vol. 26, p. 113-126Article in journal (Refereed)

4. Closed ideals in the ball algebra

Hedenmalm, Håkan

KTH, Superseded Departments, Mathematics.

Closed ideals in the ball algebra1989In: Bulletin of the London Mathematical Society, ISSN 0024-6093, E-ISSN 1469-2120, Vol. 21, p. 469-474Article in journal (Refereed)

5. Periodic points of endomorphisms on solenoids and related groups

Miles, Richard

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

This paper investigates the problem of finding the possible sequences of periodic point counts for endomorphisms of solenoids. For an ergodic epimorphism of a solenoid, a closed formula is given that expresses the number of points of any given period in terms of sets of places of finitely many algebraic number fields and distinguished elements of those fields. The result extends to more general epimorphisms of compact abelian groups.

Maximal estimates are studied for solutions to an initial value problem for the nonelliptic Schrodinger equation. A result of Rogers, Vargas and Vega is extended.