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Standard ideals in convolution Sobolev algebras on the half-line

José E. Galé, Antoni Wawrzyńczyk (2011)

Colloquium Mathematicae

We study the relation between standard ideals of the convolution Sobolev algebra ( n ) ( t ) and the convolution Beurling algebra L¹((1+t)ⁿ) on the half-line (0,∞). In particular it is proved that all closed ideals in ( n ) ( t ) with compact and countable hull are standard.

Stieltjes perfect semigroups are perfect

Torben Maack Bisgaard, Nobuhisa Sakakibara (2005)

Czechoslovak Mathematical Journal

An abelian * -semigroup S is perfect (resp. Stieltjes perfect) if every positive definite (resp. completely so) function on S admits a unique disintegration as an integral of hermitian multiplicative functions (resp. nonnegative such). We prove that every Stieltjes perfect semigroup is perfect. The converse has been known for semigroups with neutral element, but is here shown to be not true in general. We prove that an abelian * -semigroup S is perfect if for each s S there exist t S and m , n 0 such that m + n 2 ...

Strong continuity of invariant probability charges

Harald Luschgy, Sławomir Solecki (2004)

Colloquium Mathematicae

Consider a semigroup action on a set. We derive conditions, in terms of the induced action of the semigroup on {0,1}-valued probability charges, which ensure that all invariant probability charges are strongly continuous.

Strong convergence theorems for two-parameter Walsh-Fourier and trigonometric-Fourier series

Ferenc Weisz (1996)

Studia Mathematica

The martingale Hardy space H p ( [ 0 , 1 ) 2 ) and the classical Hardy space H p ( 2 ) are introduced. We prove that certain means of the partial sums of the two-parameter Walsh-Fourier and trigonometric-Fourier series are uniformly bounded operators from H p to L p (0 < p ≤ 1). As a consequence we obtain strong convergence theorems for the partial sums. The classical Hardy-Littlewood inequality is extended to two-parameter Walsh-Fourier and trigonometric-Fourier coefficients. The dual inequalities are also verified and a...

Strong stabilization of controlled vibrating systems

Jean-François Couchouron (2011)

ESAIM: Control, Optimisation and Calculus of Variations

This paper deals with feedback stabilization of second order equations of the form ytt + A0y + u (t) B0y (t) = 0, t ∈ [0, +∞[, where A0 is a densely defined positive selfadjoint linear operator on a real Hilbert space H, with compact inverse and B0 is a linear map in diagonal form. It is proved here that the classical sufficient ad-condition of Jurdjevic-Quinn and Ball-Slemrod with the feedback control u = ⟨yt, B0y⟩H implies the strong stabilization. This result is derived from a general compactness...

Strong stabilization of controlled vibrating systems

Jean-François Couchouron (2011)

ESAIM: Control, Optimisation and Calculus of Variations

This paper deals with feedback stabilization of second order equations of the form ytt + A0y + u (t) B0y (t) = 0, t ∈ [0, +∞[, where A0 is a densely defined positive selfadjoint linear operator on a real Hilbert space H, with compact inverse and B0 is a linear map in diagonal form. It is proved here that the classical sufficient ad-condition of Jurdjevic-Quinn and Ball-Slemrod with the feedback control u = ⟨yt, B0y⟩H implies the strong stabilization. This result is derived from a general compactness theorem...

Strongly invariant means on commutative hypergroups

Rupert Lasser, Josef Obermaier (2012)

Colloquium Mathematicae

We introduce and study strongly invariant means m on commutative hypergroups, m ( T x φ · ψ ) = m ( φ · T x ̃ ψ ) , x ∈ K, φ , ψ L ( K ) . We show that the existence of such means is equivalent to a strong Reiter condition. For polynomial hypergroups we derive a growth condition for the Haar weights which is equivalent to the existence of strongly invariant means. We apply this characterization to show that there are commutative hypergroups which do not possess strongly invariant means.

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