1,721,008 research outputs found
Henstock-Kurzweil type integrals on zero-dimensional groups and its application in Harmonic Analysis
No full textWe introduce here a Henstock type integral on compact subsets of a locally compact zero-dimensional abelian group and we use this integral to solve the problem of recovering the coefficients of convergent series with respect to characters of a compact zero dimensional abelian group and to obtain an inversion formula for multiplicative integral transform with a kernel expressed in terms of characters of a locally compact zero dimensional abelian group
Multidimensional P-adic Integrals in some Problems of Harmonic Analysis
No full textThe paper is a survey of results related to the problem of recovering the coefficients of some classical orthogonal series from their sums by generalized Fourier formulas. The method is based on reducing the coefficient problem to the one of recovering a function from its derivative with respect to an appropriate derivation basis. In the case of the multiple Vilenkin system the problem is solved by using a multidimensional P-adic integral
On the possible values of upper and lower derivatives with respect to differentiation bases of product structure.
No full textA solution of the Guzmán's problem on possible values of upper and lower derivatives
is given for the class of translation invariant and product type differentiation bases formed by ndimensional
intervals. Namely, the bases from the mentioned class are characterized, for which
integral means of a summable function can boundedly diverge only on a set of zero measur
A version of Hake's theorem for Kurzweil-Henstock integral in terms of variational measure
Get PDFWe introduce the notion of variational measure with respect to a derivation basis in a topological measure space and consider a Kurzweil-Henstock-type integral related to this basis. We prove a version of Hake's theorem in terms of a variational measure
Dual of the Class of HKr Integrable Functions
No full textWe define for 1 <= r < infinity a norm for the class of functions which are Henstock-Kurzweil integrable in the L-r sense. We then establish that the dual in this norm is isometrically isomorphic to L-r' and is therefore a Banach space, and in the case r = 2, a Hilbert space. Finally, we give results pertaining to convergence and weak convergence in this space
On the Almost Everywhere Convergence of Multiple Fourier-Haar Series
No full textThe paper deals with the question of convergence of multiple Fourier-Haar series with partial sums taken over homothetic copies of a given convex bounded set W⊂R+n containing the intersection of some neighborhood of the origin with R+n. It is proved that for this type sets W with symmetric structure it is guaranteed almost everywhere convergence of Fourier-Haar series of any function from the class L(ln+L)n−1
On Descriptive Characterizations of an Integral Recovering a Function from Its -Derivative
No full textThe notion of Lr-variational measure generated by a function F ∈ Lr[a, b] is introduced and, in terms of absolute continuity of this measure, a descriptive characterization of the HKr -integral recovering a function from its Lr-derivative is given. It is shown that the class of functions generating absolutely continuous Lr-variational measure coincides with the class of ACGr -functions which was introduced earlier, and that both classes coincide with the class of the indefinite HKr-integrals under the assumption of Lr-differentiability almost everywhere of the functions consisting these classe
THE HKr-INTEGRAL IS NOT CONTAINED IN THE Pr-INTEGRAL
Get PDFWe compare a Perron-type integral with a Henstock-Kurzweiltype integral, both having been introduced to recover functions from their generalized derivatives defined in the metric Lr. We give an example of an HKr-integrable function which is not Pr-integrable, thereby showing that the first integral is strictly wider than the second one
Kurzweil-Henstock type integral on zero-dimensional group and some of its applications
Get PDFsummary:A Kurzweil-Henstock type integral on a zero-dimensional abelian group is used to recover by generalized Fourier formulas the coefficients of the series with respect to the characters of such groups, in the compact case, and to obtain an inversion formula for multiplicative integral transforms, in the locally compact case
An existence result for fractional Kirchhoff-type equations
Get PDFThe aim of this paper is to study a class of nonlocal fractional Laplacian equations of Kirchhoff-type. More precisely, by using an appropriate analytical context on fractional Sobolev spaces, we establish the existence of one non-trivial weak solution for nonlocal fractional problems exploiting suitable variational methods
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