Some remarks an interpolation of operators and Fourier coefficients
Some remarks on a theorem of S.M. Lozinski concerning linear process of approximation of periodic functions
Some remarks on quasi-Cohen sets
We are interested in Banach space geometry characterizations of quasi-Cohen sets. For example, it turns out that they are exactly the subsets E of the dual of an abelian compact group G such that the canonical injection is a 2-summing operator. This easily yields an extension of a result due to S. Kwapień and A. Pełczyński. We also investigate some properties of translation invariant quotients of L¹ which are isomorphic to subspaces of L¹.
Some remarks on sets of uniform convergence
Some remarks on strong approximation by Cesàro means
Some results about the Henstock-Kurzweil Fourier transform
We consider the Fourier transform in the space of Henstock-Kurzweil integrable functions. We prove that the classical results related to the Riemann-Lebesgue lemma, existence and continuity are true in appropriate subspaces.
Some results in spectral analysis and synthesis at infinity.
Some results in the metric theory of tensor products
Some results on -approximation of the -th derivate of Fourier series.
Some singular measures on the circle which improve spaces
Some spherical uniqueness theorems for multiple trigonometric series.
Some types of lacunary Fourier series
Sommes partielles des séries de Fourier
Sous-espaces de invariants par translation et de type
Spaces of functions of generalized bounded variation. II: Questions of uniform convergence of Fourier series.
Spaces of Test Functions and Theorems of the Bochner-Schoenberg-Eberlein Type.
Spectra of elements in the group ring of SU(2)
We present a new method for establishing the ‘‘gap” property for finitely generated subgroups of , providing an elementary solution of Ruziewicz problem on as well as giving many new examples of finitely generated subgroups of with an explicit gap. The distribution of the eigenvalues of the elements of the group ring in the -th irreducible representation of is also studied. Numerical experiments indicate that for a generic (in measure) element of , the “unfolded” consecutive spacings...
Spectral analysis for rank one perturbations of diagonal operators in non-archimedean Hilbert space
The paper is concerned with the spectral analysis for the class of linear operators in non-archimedean Hilbert space, where is a diagonal operator and is a rank one operator. The results of this paper turn out to be a generalization of those results obtained by Diarra.
Spectral decompositions and harmonic analysis on UMD spaces
We develop a spectral-theoretic harmonic analysis for an arbitrary UMD space X. Our approach utilizes the spectral decomposability of X and the multiplier theory for to provide on the space X itself analogues of the classical themes embodied in the Littlewood-Paley Theorem, the Strong Marcinkiewicz Multiplier Theorem, and the M. Riesz Property. In particular, it is shown by spectral integration that classical Marcinkiewicz multipliers have associated transforms acting on X.
Spectral decompositions, ergodic averages, and the Hilbert transform
Let U be a trigonometrically well-bounded operator on a Banach space , and denote by the sequence of (C,2) weighted discrete ergodic averages of U, that is, . We show that this sequence of weighted ergodic averages converges in the strong operator topology to an idempotent operator whose range is x ∈ : Ux = x, and whose null space is the closure of (I - U). This result expands the scope of the traditional Ergodic Theorem, and thereby serves as a link between Banach space spectral theory and...