C1 Changes of Variable: Beurling-Helson Type Theorem and Hörmander Conjecture on Fourier Multipliers.
Calderón's Formula Associated with a Differential Operator on (0, ...) and Inversion of the Generalized Abel Transform.
Carleson's Theorem: proof, complements, variations.
Carleson's Theorem from 1965 states that the partial Fourier sums of a square integrable function converge pointwise. We prove an equivalent statement on the real line, following the method developed by the author and C. Thiele. This theorem, and the proof presented, is at the center of an emerging theory which complements the statement and proof of Carleson's theorem. An outline of these variations is also given.
Causality and local analyticity : mathematical study
Characterization of measures in the group C*-algebra of a locally compact group.
Complex powers and asymptotic expansions. I. Functions of certain types.
Complex powers and asymptotic expansions. II.
Continuous linear right inverses for convolution operators in spaces of real analytic functions
We determine the convolution operators on the real analytic functions in one variable which admit a continuous linear right inverse. The characterization is given by means of a slowly decreasing condition of Ehrenpreis type and a restriction of hyperbolic type on the location of zeros of the Fourier transform μ̂(z).
Corrections to the Papers "Power Bounded Matrices of Fourier-Stieltjes Transforms I, II".
Counterexamples for classical operators on Lorentz-Zygmund spaces
Critical length for a Beurling type theorem
In a recent paper [3] C. Baiocchi, V. Komornik and P. Loreti obtained a generalisation of Parseval's identity by means of divided differences. We give here a proof of the optimality of that theorem.