Regularized Summation of Haar Series of Continuous Functions

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Home Editorial board Publication ethics Peer review guidelines Latest issue All issues Rules for authors Online submission system's guidelines Submit manuscript Contacts Address: Vatutina st. 53, Vladikavkaz, 362025, RNO-A, Russia Phone: (8672)23-00-54 E-mail: rio@smath.ru	DOI: 10.23671/VNC.2016.2.5918 Regularized Summation of Haar Series of Continuous Functions Kazarian M. L. Vladikavkaz Mathematical Journal 2016. Vol. 18. Issue 2. Abstract: We study the problem of summation of Haar series of continuous functions. We present the proof of the stability and uniform convergence of Haar series regularized by generalized summation function for the class of continuous functions with approximate coefficients. Keywords: Haar transformation, Haar series, Tikhonov regularization method, regularizing multiplier, class of functions \(S_p\), \(1\leq p<\infty\). Language: Russian Download the full text For citation: Kazarian M. L. Regularized summation of Haar series of continuous functions // Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 19, no. 2, pp. 49-54. DOI 10.23671/VNC.2016.2.5918 + References 1. Kazarjan M. L. Issledovanie zadach cifrovoj obrabotki signalov posredstvom diskretnyh ortogonal'nyh preobrazovanij na ustojchivost' [Research of Digital Signal Processing Problems by a Discrete Orthogonal Transformation on Sustainability. A Monograph]. Vladikavkaz, NOSU, 2009. 81p. [in Russian]. 2. Kazarjan M. L. Haar Wavelet Transformation in the Telecommunications System and their Research on Sustainability. Telekommunikacii [The Telecommunications], 2014, no. 9, pp.7-13. [in Russian]. 3. Prjett U. Tsifrovaya obrabotka izobrazheniy [Digital Image Processing]. Moscow, Mir, 1982. [in Russian]. 4. Sobol' I. M. Mnogomernye kvadraturnye formuly i funkcii Haara [Multidimensional Quadrature Formulas and Haar's Functions]. Moscow, Nauka, 1969. 288 p. [in Russian]. 5. Tihonov A. N On sustainable methods of summation of Fourier series. Doklady AN SSSR [Reports of the USSR Academy of Sciences], 1964, vol. 156. no. 2. pp. 268-271 [in Russian]. 6. Fihtengol'c G. M. Kurs differencial'nyh i integral'nyh ischislenij. T. 2 [Course of Differential and Integral Calculus. Vol. 2]. Moscow, Nauka, 1964. 463 p. 7. Haar A. Zur Theoria der orthogonalen Funktionsysteme. Math. Fnn. 1910, vol. 69. pp. 331-371. 8. Shovengerdt R. A. Distancionnoe zondirovanie. Metody i modeli obrabotki izobrazhenij [Remote Sensing. Models and Metods for Image Processing]. Moscow, Tekhnosfera, 2010. 560 p. The sole copyright holder of the published work is the Founder of the Vladikavkaz Mathematical Journal. The terms of use of this work are governed by an open license (Creative Commons Attribution-NonCommercial 4.0 International). The use of metadata of the scientific article, including the title, abstract, author information, references, identifiers, and other bibliographic description elements for subsequent unrestricted use, is carried out under the terms of the CC BY or CC0 open licenses. ← Contents of issue


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