Contributions to harmonic analysis
نویسندگان
چکیده
منابع مشابه
Contributions of Proximate Determinants to Fertility Transition in Bangladesh: An Analysis of Bongaarts’ Fertility Model
Introduction: Fertility transition is outright by prime four proximate determinants (marriage, contraception, postpartum infecundability, and abortion). The present study examines the contributions of proximate determinants on fertility decline and quantifies inhibiting the effect of major proximate determinants according to the socioeconomic characteristics in Bangladesh.<br /...
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Analysis in general tends to revolve around the study of general classes of functions (often real-valued or complex-valued) and operators (which take one or more functions as input, and return some other function as output). Harmonic analysis focuses in particular on the quantitative properties of such functions, and how these quantitative properties change when apply various (often quite expli...
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We use τK to denote the topology of DK (Ω) equipped with such metric. The topology of D (Ω) can be defined precisely. Let β be the collection of all convex balanced sets W ⊂ D (Ω) such that DK (Ω) ∩ W ∈ τK for every compact K ⊂ Ω. Let τ be the collection of all unions of sets of the form φ+W with φ ∈ D (Ω) and W ∈ β. Theorem 1. τ is a topology in D (Ω) and β is a local base for τ . The topology...
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1. (f̂ + g)(ξ) = f̂(ξ) + ĝ(ξ). 2. For any α ∈ C, (α̂f)(ξ) = αf̂(ξ). 3. Let f̄ denote the complex conjugate of f . Then ˆ̄ f(ξ) = f̂(ξ). 4. For λ ∈ R \ {0}, denote fλ(x) = λf(λx). Then f̂λ(ξ) = f̂( ξ λ ). 5. For y ∈ R let (τyf)(t) = f(t− y). Then τ̂yf(ξ) = f̂(ξ)e−2πiξy. 6. |f̂(ξ)| ≤ ‖f‖L1(R). Definition 1.3. The Schwartz space, S(R), is the space of C∞ functions that are rapidly decreasing, in the sense that
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Harmonic analysis studies the representation of functions as the linear combination of basic wave-like functions. It plays a fundamental role in the processing of time-series signals and images. Recent years have witnessed many efforts to adapt the Fourier and wavelet analysis to the domain of 3D shapes. The manifold Fourier analysis relies on the eigenfunctions of the Laplace-Beltrami operator...
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ژورنال
عنوان ژورنال: Acta Mathematica
سال: 1956
ISSN: 0001-5962
DOI: 10.1007/bf02392363