Henstock-kurzweil Type Integrals in P-adic Harmonic Analysis
نویسنده
چکیده
Some recent results related to the P-adic derivatives and integrals are surveyed. Applications of the Henstock-Kurzweil P-integral and the Perron P-integral to the problem of recovering the coefficients of series with respect to the Vilenkin system and the Haar system (both in one dimension and in higher dimensions) are discussed. The case of the continual analogue of the Vilenkin system is also considered.
منابع مشابه
Henstock–Kurzweil delta and nabla integrals
We will study the Henstock–Kurzweil delta and nabla integrals, which generalize the Henstock–Kurzweil integral. Many properties of these integrals will be obtained. These results will enable time scale researchers to study more general dynamic equations. The Hensock–Kurzweil delta (nabla) integral contains the Riemann delta (nabla) and Lebesque delta (nabla) integrals as special cases.
متن کاملSubstitution Formulas for the Kurzweil and Henstock Vector Integrals
Results on integration by parts and integration by substitution for the variational integral of Henstock are well-known. When real-valued functions are considered, such results also hold for the Generalized Riemann Integral defined by Kurzweil since, in this case, the integrals of Kurzweil and Henstock coincide. However, in a Banach-space valued context, the Kurzweil integral properly contains ...
متن کاملOn Belated Differentiation and a Characterization of Henstock-kurzweil-ito Integrable Processes
The Henstock-Kurzweil approach, also known as the generalized Riemann approach, has been successful in giving an alternative definition to the classical Itô integral. The Riemann approach is well-known for its directness in defining integrals. In this note we will prove the Fundamental Theorem for the Henstock-Kurzweil-Itô integral, thereby providing a characterization of Henstock-Kurzweil-Itô ...
متن کاملHenstock–Kurzweil Fourier transforms
The Fourier transform is considered as a Henstock–Kurzweil integral. Sufficient conditions are given for the existence of the Fourier transform and necessary and sufficient conditions are given for it to be continuous. The Riemann–Lebesgue lemma fails: Henstock– Kurzweil Fourier transforms can have arbitrarily large point-wise growth. Convolution and inversion theorems are established. An appen...
متن کاملIntegro-differential Equations on Time Scales with Henstock-kurzweil Delta Integrals
In this paper we prove existence theorems for integro – differential equations x(t) = f(t, x(t), ∫ t 0 k(t, s, x(s))∆s), x(0) = x0 t ∈ Ia = [0, a] ∩ T, a ∈ R+, where T denotes a time scale (nonempty closed subset of real numbers R), Ia is a time scale interval. Functions f, k are Carathéodory functions with values in a Banach space E and the integral is taken in the sense of Henstock-Kurzweil d...
متن کامل