On a Class of Three Dimensional Radially Symmetric Positive Definite Functions.
On a generalization of Hankel kernel.
On a Hilbert-type transform
On a Multiplier Transform
On a property of the Fourier transform.
On approximation of locally compact groups by finite algebraic systems.
On bilinear Littlewood-Paley square functions.
On the real line, let the Fourier transform of kn be k'n(ξ) = k'(ξ-n) where k'(ξ) is a smooth compactly supported function. Consider the bilinear operators Sn(f, g)(x) = ∫ f(x+y)g(x-y)kn(y) dy. If 2 ≤ p, q ≤ ∞, with 1/p + 1/q = 1/2, I prove thatΣ∞n=-∞ ||Sn(f,g)||22 ≤ C2||f||p2||g||q2.The constant C depends only upon k.
On discrete Fourier spectrum of a harmonic with random frequency modulation
Asymptotic properties of the Discrete Fourier Transform spectrum of a complex monochromatic oscillation with frequency randomly distorted at the observation times t=0,1,..., n-1 by a series of independent and identically distributed fluctuations is investigated. It is proved that the second moments of the spectrum at the discrete Fourier frequencies converge uniformly to zero as n → ∞ for certain frequency fluctuation distributions. The observed effect occurs even for frequency fluctuations with...
On Dualizing a Multivariable Poisson Summation Formula.
On Fourier coefficients and transforms of functions of two variables
On Fourier-Stieltjes transforms integer-valued on a given subset.
On generation and propagation of tsunamis in a shallow running ocean.
On Heisenberg and local uncertainty principles for the -Dunkl transform.
On High Precision Methods for the Evaluation of Fourier Integrals with Finite and Infinite Limits.
On instances of Fox’s integral equation connection to the Riemann zeta function
We consider some applications of the singular integral equation of the second kind of Fox. Some new solutions to Fox’s integral equation are discussed in relation to number theory.
On Littlewood-Paley functions
On some classes of distributions
On the absolute convergence of small gaps Fourier series of functions of .
On the coefficients in Fourier-Stieltjes series with norm-bounded partial sums
On the Dirichlet and Neumann problems in multi-dimensional cone
We consider an elliptic pseudodifferential equation in a multi-dimensional cone, and using the wave factorization concept for an elliptic symbol we describe a general solution of such equation in Sobolev-Slobodetskii spaces. This general solution depends on some arbitrary functions, their quantity being determined by an index of the wave factorization. For identifying these arbitrary functions one needs some additional conditions, for example, boundary conditions. Simple boundary value problems,...