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,...
On the Fourier transform of
On the Fourier transform of the symmetric decreasing rearrangements
Inspired by work of Montgomery on Fourier series and Donoho-Strak in signal processing, we investigate two families of rearrangement inequalities for the Fourier transform. More precisely, we show that the behavior of a Fourier transform of a function over a small set is controlled by the behavior of the Fourier transform of its symmetric decreasing rearrangement. In the case, the same is true if we further assume that the function has a support of finite measure.As a byproduct, we also give...
On The Frequency With Which Bounded Functions Have Spectral Gaps
On the generalized Fourier transforms associated with Schrödinger operators with long-range perturbations.
On the Heisenberg-Pauli-Weyl inequality.
On the Heisenberg-Weyl inequality.
On the integrability of a class of integral transforms
On the integrability of Walsh-Fourier transform.
On The Interpolation Between Certain Theorems On Fourier Transforms.
On the polyconvolution with the weight function for the Fourier cosine, Fourier sine, and the Kontorovich-Lebedev integral transforms.
On the refined Heisenberg-Weyl type inequality.
On the regular Sturm-Liouville transform.
On the theorem of Ivasev-Musatov. I
We give a new version of Ivasev-Musatov’s construction of a measure whose support has Lebesgue measure zero but whose Fourier transform drops away extremely rapidly.
On the theorem of Ivasev-Musatov. II
As in Part I [Annales de l’Inst. Fourier, 27-3 (1997), 97-113], our object is to construct a measure whose support has Lebesgue measure zero, but whose Fourier transform drops away extremely fast.
On the Translation Invariance of Wavelet Subspaces.
Opérateurs de Fourier