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Mat. Sb., 2007, Volume 198, Number 2, Pages 67–90 (Mi msb3780)  

This article is cited in 4 scientific papers (total in 4 papers)

Dyadic distributions

B. I. Golubov

Moscow Engineering Physics Institute (State University)

Abstract: On the basis of the concept of pointwise dyadic derivative dyadic distributions are introduced as continuous linear functionals on the linear space $D_d(\mathbb R_+)$ of infinitely differentiable functions compactly supported by the positive half-axis $\mathbb R_+$ together with all dyadic derivatives. The completeness of the space $D'_d(\mathbb R_+)$ of dyadic distributions is established. It is shown that a locally integrable function on $\mathbb R_+$ generates a dyadic distribution.
In addition, the space $S_d(\mathbb R_+)$ of infinitely dyadically differentiable functions on $\mathbb R_+$ rapidly decreasing in the neighbourhood of $+\infty$ is defined. The space $S'_d(\mathbb R_+)$ of dyadic distributions of slow growth is introduced as the space of continuous linear functionals on $S_d(\mathbb R_+)$. The completeness of the space $S'_d(\mathbb R_+)$ is established; it is proved that each integrable function on $\mathbb R_+$ with polynomial growth at $+\infty$ generates a dyadic distribution of slow growth.
Bibliography: 25 titles.

DOI: https://doi.org/10.4213/sm3780

Full text: PDF file (648 kB)
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English version:
Sbornik: Mathematics, 2007, 198:2, 207–230

Bibliographic databases:

UDC: 517.982.4
MSC: 46F05, 42C10
Received: 18.04.2005 and 30.10.2006

Citation: B. I. Golubov, “Dyadic distributions”, Mat. Sb., 198:2 (2007), 67–90; Sb. Math., 198:2 (2007), 207–230

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. S. Volosivets, “Applications of $\mathbf P$-adic generalized functions and approximations by a system of $\mathbf P$-adic translations of a function”, Siberian Math. J., 50:1 (2009), 1–13  mathnet  crossref  mathscinet  isi  elib
    2. S. S. Platonov, “An Analog of Titchmarsh's Theorem for the Fourier–Walsh Transform”, Math. Notes, 103:1 (2018), 96–103  mathnet  crossref  crossref  isi  elib
    3. S. S. Platonov, “On the Fourier–Walsh Transform of Functions from Dyadic Dini–Lipschitz Classes on the Semiaxis”, Math. Notes, 108:2 (2020), 229–242  mathnet  crossref  crossref  isi
    4. M. A. Karapetyants, V. Yu. Protasov, “O prostranstvakh dvoichno-obobschennykh funktsii”, Funkts. analiz i ego pril., 54:4 (2020), 56–63  mathnet  crossref
  • Математический сборник Sbornik: Mathematics (from 1967)
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