O aproximací obrazu v Hilbertově transformací ortogonálními řadami racionálních lomených funkcí
On 1-regular ordinary differential operators
Solutions to singular linear ordinary differential equations with analytic coefficients are found in the form of Laplace type integrals.
On a Hilbert-type transform
On a new approach to convolution constructions.
On a new integral transform and differential equations.
On a non-self adjoint eigenfunction expansion.
On a non-self adjoint expansion formula.
On a testing-function space for distributions associated with the Kontorovich-Lebedev transform.
We construct a testing function space, which is equipped with the topology that is generated by Lν,p - multinorm of the differential operatorAx = x2 - x d/dx [x d/dx],and its k-th iterates Akx, where k = 0, 1, ... , and A0xφ = φ. Comparing with other testing-function spaces, we introduce in its dual the Kontorovich-Lebedev transformation for distributions with respect to a complex index. The existence, uniqueness, imbedding and inversion properties are investigated. As an application we find a solution...
On a theorem of Kłosowska about generalised convolutions
On a variant of the Meijer integral transformation
On an integral transform.
On an integral transform.
On an integral transform by R. S. Phillips
The properties of a transformation by R.S. Phillips, which transforms an exponentially bounded C 0-semigroup of operators T(t) to a Yosida approximation depending on h, are studied. The set of exponentially bounded, continuous functions f: [0, ∞[→ E with values in a sequentially complete L c-embedded space E is closed under the transformation. It is shown that for certain complex h and k, and that , where the limit is uniform in t on compact subsets of the positive real line. If f is Hölder-continuous...
On asymptotic expansions of Kratzel's integral transforms
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 Calderón's conjecture.
On certain properties of Hankel transform
On conditions for the boundedness of the Weyl fractional integral on weighted spaces
In this paper we give a sufficient condition on the pair of weights for the boundedness of the Weyl fractional integral from into . Under some restrictions on and , this condition is also necessary. Besides, it allows us to show that for any there exist non-trivial weights such that is bounded from into itself, even in the case .
On conjugate Poisson integrals and Riesz transforms for the Hermite expansions
On defining the generalized functions and .