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Displaying 1621 – 1640 of 2300

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Restricting cuspidal representations of the group of automorphisms of a homogeneous tree

Donald I. Cartwright, Gabriella Kuhn (2003)

Bollettino dell'Unione Matematica Italiana

Let X be a homogeneous tree in which every vertex lies on q + 1 edges, where q 2 . Let A = A u t X be the group of automorphisms of X , and let H be the its subgroup P G L 2 , F , where F is a local field whose residual field has order q . We consider the restriction to H of a continuous irreducible unitary representation π of A . When π is spherical or special, it was well known that π remains irreducible, but we show that when π is cuspidal, the situation is much more complicated. We then study in detail what happens when the...

Riesz potentials and amalgams

Michael Cowling, Stefano Meda, Roberta Pasquale (1999)

Annales de l'institut Fourier

Let ( M , d ) be a metric space, equipped with a Borel measure μ satisfying suitable compatibility conditions. An amalgam A p q ( M ) is a space which looks locally like L p ( M ) but globally like L q ( M ) . We consider the case where the measure μ ( B ( x , ρ ) of the ball B ( x , ρ ) with centre x and radius ρ behaves like a polynomial in ρ , and consider the mapping properties between amalgams of kernel operators where the kernel ker K ( x , y ) behaves like d ( x , y ) - a when d ( x , y ) 1 and like d ( x , y ) - b when d ( x , y ) 1 . As an application, we describe Hardy–Littlewood–Sobolev type regularity theorems...

Riesz transforms for Dunkl transform

Bechir Amri, Mohamed Sifi (2012)

Annales mathématiques Blaise Pascal

In this paper we obtain the L p -boundedness of Riesz transforms for the Dunkl transform for all 1 < p < .

Rudin-like sets and hereditary families of compact sets

Étienne Matheron, Miroslav Zelený (2005)

Fundamenta Mathematicae

We show that a comeager Π₁¹ hereditary family of compact sets must have a dense G δ subfamily which is also hereditary. Using this, we prove an “abstract” result which implies the existence of independent ℳ ₀-sets, the meagerness of ₀-sets with the property of Baire, and generalizations of some classical results of Mycielski. Finally, we also give some natural examples of true F σ δ sets.

Currently displaying 1621 – 1640 of 2300