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Shift-modulation invariant spaces on LCA groups

Carlos Cabrelli, Victoria Paternostro (2012)

Studia Mathematica

A (K,Λ) shift-modulation invariant space is a subspace of L²(G) that is invariant under translations along elements in K and modulations by elements in Λ. Here G is a locally compact abelian group, and K and Λ are closed subgroups of G and the dual group Ĝ, respectively. We provide a characterization of shift-modulation invariant spaces when K and Λ are uniform lattices. This extends previous results known for L ² ( ℝ d ) . We develop fiberization techniques and suitable range functions adapted to LCA groups...

Some results about Beurling algebras with applications to operator theory

Thomas Vils Pedersen (1995)

Studia Mathematica

We prove that certain maximal ideals in Beurling algebras on the unit disc have approximate identities, and show the existence of functions with certain properties in these maximal ideals. We then use these results to prove that if T is a bounded operator on a Banach space X satisfying ∥ T n ∥ = O ( n β ) as n → ∞ for some β ≥ 0, then ∑ n = 1 ∞ ∥ ( 1 - T ) n x ∥ / ∥ ( 1 - T ) n - 1 x ∥ diverges for every x ∈ X such that ( 1 - T ) [ β ] + 1 x ≠ 0 .

Spaces of sequences, sampling theorem, and functions of exponential type

Rodolfo Torres (1991)

Studia Mathematica

We introduce certain spaces of sequences which can be used to characterize spaces of functions of exponential type. We present a generalized version of the sampling theorem and a "nonorthogonal wavelet decomposition" for the elements of these spaces of sequences. In particular, we obtain a discrete version of the so-called φ-transform studied in [6] [8]. We also show how these new spaces and the corresponding decompositions can be used to study multiplier operators on Besov spaces.

Spectral multipliers for a distinguished Laplacian on certain groups of exponential growth

Michael Cowling, Saverio Giulini, Andrzej Hulanicki, Giancarlo Mauceri (1994)

Studia Mathematica

We prove that on Iwasawa AN groups coming from arbitrary semisimple Lie groups there is a Laplacian with a nonholomorphic functional calculus, not only for L 1 ( A N ) , but also for L p ( A N ) , where 1 < p < ∞. This yields a spectral multiplier theorem analogous to the ones known for sublaplacians on stratified groups.

Spectral subspaces for the Fourier algebra

K. Parthasarathy, R. Prakash (2007)

Colloquium Mathematicae

In this note we define and explore, à la Godement, spectral subspaces of Banach space representations of the Fourier-Eymard algebra of a (nonabelian) locally compact group.

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