spaces in tubes and distributional boundary values
spaces over open subsets of
Hamilton’s Principle with Variable Order Fractional Derivatives
MSC 2010: 26A33, 70H25, 46F12, 34K37 Dedicated to 80-th birthday of Prof. Rudolf GorenfloWe propose a generalization of Hamilton’s principle in which the minimization is performed with respect to the admissible functions and the order of the derivation. The Euler–Lagrange equations for such minimization are derived. They generalize the classical Euler-Lagrange equation. Also, a new variational problem is formulated in the case when the order of the derivative is defined through a constitutive equation....
Hankel complementary integral transformations of arbitrary order.
Hankel convolution on distribution spaces with exponential growth
We study the Hankel transformation and Hankel convolution on spaces of distributions with exponential growth.
Hankel integral transforms of a new space of generalized functions of slow growth
Hankel transform on Lorentz spaces
Hankel transforms in generalized Fock spaces.
Harmonic analysis on the one-sheet hyperboloid and multiperipheral inclusive distributions
Harmonic spaces associated with adjoints of linear elliptic operators
Let be an elliptic linear operator in a domain in . We imposse only weak regularity conditions on the coefficients. Then the adjoint exists in the sense of distributions, and we start by deducing a regularity theorem for distribution solutions of equations of type given distribution. We then apply to R.M. Hervé’s theory of adjoint harmonic spaces. Some other properties of are also studied. The results generalize earlier work of the author.
Heaviside's theory of signal transmission on submarine cables
As written in L. Schwartz' book, Heaviside's theory of cables is an important source of the theory of generalized functions. The partial differential equations he discussed were the usual heat equation and the simplest hyperbolic equations of one space dimension, but he had to solve them as evolution equations in the unusual direction of the distance along which the electric signals propagate. Although he obtained explicit expressions of solutions, which were of great economical values, it has not...
Hereditarily periodic distributions
Hermitean ultradistributions.
Herz-Type Hardy Spaces for the Dunkl Operator on the Real Line
2000 Mathematics Subject Classification: Primary 46F12, Secondary 44A15, 44A35We introduce some new weighted Herz spaces associated with the Dunkl operator on R. Also we characterize by atomic decompositions the corresponding Herz-type Hardy spaces. As applications we investigate the Dunkl transform on these spaces and establish a version of Hardy inequality for this transform.* The authors are supported by the DGRST research project 04/UR/15-02.
Hilbert space valued generalized random processes. II.
Hilbert Spaces of Distributions Having an Orthogonal Basis of Exponentials.
Hilbert transform and singular integrals on the spaces of tempered ultradistributions
The Hilbert transform on the spaces of tempered ultradistributions is defined, uniquely in the sense of hyperfunctions, as the composition of the classical Hilbert transform with the operators of multiplying and dividing a function by a certain elliptic ultrapolynomial. We show that the Hilbert transform of tempered ultradistributions defined in this way preserves important properties of the classical Hilbert transform. We also give definitions and prove properties of singular integral operators...
Hilbert transformation of Beurling ultradistributions
Holomorphic Approximation and Hyperfunction Theory on a C1 Totally Real Submanifold of a Complex Manifold.
Holomorphic extension maps for spaces of Whitney jets.
The key result (Theorem 1) provides the existence of a holomorphic approximation map for some space of C∞-functions on an open subset of Rn. This leads to results about the existence of a continuous linear extension map from the space of the Whitney jets on a closed subset F of Rn into a space of holomorphic functions on an open subset D of Cn such that D ∩ Rn = RnF.