Displaying 141 – 160 of 222

Showing per page

Continuity of halo functions associated to homothecy invariant density bases

Oleksandra Beznosova, Paul Hagelstein (2014)

Colloquium Mathematicae

Let be a collection of bounded open sets in ℝⁿ such that, for any x ∈ ℝⁿ, there exists a set U ∈ of arbitrarily small diameter containing x. The collection is said to be a density basis provided that, given a measurable set A ⊂ ℝⁿ, for a.e. x ∈ ℝⁿ we have l i m k 1 / | R k | R k χ A = χ A ( x ) for any sequence R k of sets in containing x whose diameters tend to 0. The geometric maximal operator M associated to is defined on L¹(ℝⁿ) by M f ( x ) = s u p x R 1 / | R | R | f | . The halo function ϕ of is defined on (1,∞) by ϕ ( u ) = s u p 1 / | A | | x : M χ A ( x ) > 1 / u | : 0 < | A | < and on [0,1] by ϕ(u) = u. It is shown that the halo...

Continuous wavelet transform on semisimple Lie groups and inversion of the Abel transform and its dual.

K. Trimèche (1996)

Collectanea Mathematica

In this work we define and study wavelets and continuous wavelet transform on semisimple Lie groups G of real rank l. We prove for this transform Plancherel and inversion formulas. Next using the Abel transform A on G and its dual A*, we give relations between the continuous wavelet transform on G and the classical continuous wavelet transform on Rl, and we deduce the formulas which give the inverse operators of the operators A and A*.

Currently displaying 141 – 160 of 222