نتایج جستجو برای: henstock stieltjesintegral

تعداد نتایج: 179  

2007
T. L. GILL W. W. ZACHARY

In this paper, we survey recent progress on the constructive theory of the Feynman operator calculus. We first develop an operator version of the Henstock-Kurzweil integral, and a new Hilbert space that allows us to construct the elementary path integral in the manner originally envisioned by Feynman. After developing our time-ordered operator theory we extend a few of the important theorems of...

2004
J. J. Koliha

The existing proofs of the Fundamental theorem of calculus for Lebesgue integration typically rely either on the Vitali–Carathéodory theorem on approximation of Lebesgue integrable functions by semi-continuous functions (as in [3, 9, 12]), or on the theorem characterizing increasing functions in terms of the four Dini derivates (as in [6, 10]). Alternatively, the theorem is derived using the Pe...

2014
Luis Ángel Gutiérrez Méndez Juan Alberto Escamilla Reyna Maria Guadalupe Raggi Cárdenas Francisco Estrada García

and Applied Analysis 3 Then, as L[a, b] ⊂ HK([a, b]) it holds that dim(L[a, b]) ≤ dim(HK([a, b])) ≤ card(HK([a, b])). Therefore, by Lemma 8, Corollary 7 and the known fact that c0 = c, we obtain the desired conclusion. Hereafter, the Alexiewicz topology and the topology induced by the norm of Proposition 9 will be denoted as τ A and τ ‖⋅‖ , respectively. Proposition 10. The topology τ ‖⋅‖ on HK...

Journal: :The American Mathematical Monthly 2001
Erik Talvila

1. THE RIEMANN–LEBESGUE LEMMA. In its usual form, the Riemann– Lebesgue Lemma reads as follows: If f ∈ L1 and f̂ (s) = ∫∞ −∞ eisx f (x) dx is its Fourier transform, then f̂ (s) exists and is finite for each s ∈ R and f̂ (s) → 0 as |s| → ∞ (s ∈ R). This result encompasses Fourier sine and cosine transforms as well as Fourier series coefficients for functions periodic on finite intervals. When the i...

2010
Aneta Sikorska-Nowak

and Applied Analysis 3 We note that 1.1 in its general form involves some different types of differential and difference equations depending on the choice of the time scale T . For example: 1 for T R, we have σ t t, μ t 0, and xΔ t x′ t , and 1.1 becomes the Cauchy integrodifferential equation: x′ t f ( t, x t , ∫ t 0 k t, s, x s ds ) , t ∈ R,

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