A general theorem on Nörlund summability of Fourier series with applications
A generalization of 2-periodic trigonometric interpolation.
A Generalized Convolution with a Weight Function for the Fourier Cosine and Sine Transforms
A generalized convolution with a weight function for the Fourier cosine and sine transforms is introduced. Its properties and applications to solving a system of integral equations are considered.
A later note on the relationships of numerical sequences.
A law of the iterated logarithm for general lacunary series
We prove a law of the iterated logarithm for sums of the form where the satisfy a Hadamard gap condition. Here we assume that f is a Dini continuous function on ℝⁿ which has the property that for every cube Q of sidelength 1 with corners in the lattice ℤⁿ, f vanishes on ∂Q and has mean value zero on Q.
A limit theorem for the q-convolution
The q-convolution is a measure-preserving transformation which originates from non-commutative probability, but can also be treated as a one-parameter deformation of the classical convolution. We show that its commutative aspect is further certified by the fact that the q-convolution satisfies all of the conditions of the generalized convolution (in the sense of Urbanik). The last condition of Urbanik's definition, the law of large numbers, is the crucial part to be proved and the non-commutative...
A Littlewood-Paley inequality for arbitrary intervals.
A Littlewood-Paley Inequality for the Carleson Operator.
A lower bound in the law of the iterated logarithm for general lacunary series
We prove a lower bound in a law of the iterated logarithm for sums of the form where f satisfies certain conditions and the satisfy the Hadamard gap condition .
A majorant problem.
A method for the calculus of Bernstein's polynomial.
A systematic method for the calculus of Bernstein's polynomial is described. It consists of reducing the problem to a homogeneous linear system of equations that may be constructed by fixed rules. Several problems about its computer implementation are discussed.
A moment theory approach to the Riesz theorem on the conjugate function with general measures
A multiparameter variant of the Salem-Zygmund central limit theorem on lacunary trigonometric series
We prove the central limit theorem for the multisequence where , are reals, are partially hyperbolic commuting s × s matrices, and x is a uniformly distributed random variable in . The main tool is the S-unit theorem.
A multiplier characterization of analytic UMD spaces
A multiplier theorem for Jacobi expansions
A multiplier theorem for ultraspherical series
A new Approach to Temperate Generalized Colombeau Functions
A New Characterization of Besicovitch Almost Periodic Functions.
A new classification of periodic functions and their approximation
A new criterion for the absolute Riesz summability of the conjugate series of a Fourier series