Majorizing measures and proportional subsets of bounded orthonormal systems..
Marcinkiewicz multipliers of higher variation and summability of operator-valued Fourier series
Let , where, for 1 ≤ r < ∞, (resp., ) denotes the class of functions (resp., bounded functions) g: → ℂ such that g has bounded r-variation (resp., uniformly bounded r-variations) on (resp., on the dyadic arcs of ). In the author’s recent article [New York J. Math. 17 (2011)] it was shown that if is a super-reflexive space, and E(·): ℝ → () is the spectral decomposition of a trigonometrically well-bounded operator U ∈ (), then over a suitable non-void open interval of r-values, the condition...
Markov and Bernstein inequalities in for some weighted algebraic and trigonometric polynomials.
Matrix Refinement Equations: Existence and Uniqueness.
Maximal regularity of discrete and continuous time evolution equations
We consider the maximal regularity problem for the discrete time evolution equation for all n ∈ ℕ₀, u₀ = 0, where T is a bounded operator on a UMD space X. We characterize the discrete maximal regularity of T by two types of conditions: firstly by R-boundedness properties of the discrete time semigroup and of the resolvent R(λ,T), secondly by the maximal regularity of the continuous time evolution equation u’(t) - Au(t) = f(t) for all t > 0, u(0) = 0, where A:= T - I. By recent results of...
Mean periodic functions on phase space and the Pompeiu problem with a twist
We show that when is a mean periodic function of tempered growth on the reduced Heisenberg group then the closed translation and rotation invariant subspace generated by contains an elementary spherical function. Using a Paley-Wiener theorem for the Fourier-Weyl transform we formulate a conjecture for arbitrary mean periodic functions.
Mean-periodic functions.
Mean-Periodic Functions Associated with the Jacobi-Dunkl Operator on R
2000 Mathematics Subject Classification: 34K99, 44A15, 44A35, 42A75, 42A63Using a convolution structure on the real line associated with the Jacobi-Dunkl differential-difference operator Λα,β given by: Λα,βf(x) = f'(x) + ((2α + 1) coth x + (2β + 1) tanh x) { ( f(x) − f(−x) ) / 2 }, α ≥ β ≥ −1/2 , we define mean-periodic functions associated with Λα,β. We characterize these functions as an expansion series intervening appropriate elementary functions expressed in terms of the derivatives of the...
Mean-periodicity and zeta functions
This paper establishes new bridges between zeta functions in number theory and modern harmonic analysis, namely between the class of complex functions, which contains the zeta functions of arithmetic schemes and closed with respect to product and quotient, and the class of mean-periodic functions in several spaces of functions on the real line. In particular, the meromorphic continuation and functional equation of the zeta function of an arithmetic scheme with its expected analytic shape is shown...
Measures and lacunary sets
We establish new connections between some classes of lacunary sets. The main tool is the use of (p,q)-summing or weakly compact operators (for Riesz sets). This point of view provides new properties of stationary sets and allows us to generalize to more general abelian groups than the torus some properties of p-Sidon sets. We also construct some new classes of Riesz sets.
Mellin pseudodifferential operators with slowly varying symbols and singular integrals on Carleson curves with Muckenhoupt weights.
Mémoire sur l'approximation des fonctions de très-grands nombres, et sur une classe étendue de développements en série.
Mesures spectrales associées à certaines suites arithmétiques
Metric unconditionality and Fourier analysis
We investigate several aspects of almost 1-unconditionality. We characterize the metric unconditional approximation property (umap) in terms of “block unconditionality”. Then we focus on translation invariant subspaces and of functions on the circle and express block unconditionality as arithmetical conditions on E. Our work shows that the spaces , p an even integer, have a singular behaviour from the almost isometric point of view: property (umap) does not interpolate between and . These...
Minimal sequences and the Kadison-Singer problem.
Minimale Elemente auf Hyperebenen und konjugierte Funktionen
Modeling repulsive forces on fibres via knot energies
Modeling of repulsive forces is essential to the understanding of certain bio-physical processes, especially for the motion of DNA molecules. These kinds of phenomena seem to be driven by some sort of “energy” which especially prevents the molecules from strongly bending and forming self-intersections. Inspired by a physical toy model, numerous functionals have been defined during the past twenty-five years that aim at modeling self-avoidance. The general idea is to produce “detangled” curves having...
Modulation invariant and multilinear singular integral operators
In a series of papers beginning in the late 1990s, Michael Lacey and Christoph Thiele have resolved a longstanding conjecture of Calderón regarding certain very singular integral operators, given a transparent proof of Carleson’s theorem on the almost everywhere convergence of Fourier series, and initiated a slew of further developments. The hallmarks of these problems are multilinearity as opposed to mere linearity, and especially modulation symmetry. By modulation is meant multiplication by characters...
Moltiplicatori di Fourier e teoremi di immersione per certi spazi funzionali. II
More Epsilonized Bounds of the Boas-Kac-Lukosz Type.