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Venetis, John, Sideridis, Emilios. (1395). A contribution to approximate analytical evaluation of Fourier series via an Applied Analysis standpoint; an application in turbulence spectrum of eddies. هنرهای کاربردی, 7(2), 229-242. doi: 10.22075/ijnaa.2017.10573.1510
John Venetis; Emilios Sideridis. "A contribution to approximate analytical evaluation of Fourier series via an Applied Analysis standpoint; an application in turbulence spectrum of eddies". هنرهای کاربردی, 7, 2, 1395, 229-242. doi: 10.22075/ijnaa.2017.10573.1510
Venetis, John, Sideridis, Emilios. (1395). 'A contribution to approximate analytical evaluation of Fourier series via an Applied Analysis standpoint; an application in turbulence spectrum of eddies', هنرهای کاربردی, 7(2), pp. 229-242. doi: 10.22075/ijnaa.2017.10573.1510
Venetis, John, Sideridis, Emilios. A contribution to approximate analytical evaluation of Fourier series via an Applied Analysis standpoint; an application in turbulence spectrum of eddies. هنرهای کاربردی, 1395; 7(2): 229-242. doi: 10.22075/ijnaa.2017.10573.1510

A contribution to approximate analytical evaluation of Fourier series via an Applied Analysis standpoint; an application in turbulence spectrum of eddies

International Journal of Nonlinear Analysis and Applications
مقاله 20، دوره 7، شماره 2، اسفند 2016، صفحه 229-242    اصل مقاله (375.1 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2017.10573.1510
نویسندگان
John Venetis1؛ Emilios Sideridis* 2
1School of Applied Mathematics and Physical Sciences NTUA, Section of Mechanics, 5 Heroes of Polytechnion Avenue GR,15773 Athens, Greece
2School of Applied Mathematics and Physical Sciences NTUA, Section of Mechanics, 5 Heroes of Polytechnion Avenue GR,15773 Athens, Greece.
تاریخ دریافت: 23 بهمن 1392،  تاریخ بازنگری: 13 آبان 1394،  تاریخ پذیرش: 09 مهر 1395 
چکیده
In the present paper, we shall attempt to make a contribution to approximate analytical evaluation of the harmonic decomposition of an arbitrary continuous function. The basic assumption is that the class of functions that we investigate here, except the verification of Dirichlet's principles, is concurrently able to be expanded in Taylor's representation, over a particular interval of their domain of definition. Thus, we shall take into account the simultaneous validity of these two properties over this interval, in order to obtain an alternative equivalent representation of the corresponding harmonic decomposition for this category of functions. In the sequel, we shall also implement this resultant formula in the investigation of turbulence spectrum of eddies according to known from literature Von Karman's formulation, making the additional assumption that during the evolution of such stochastic dynamic effects with respect to time, the occasional time-returning period can be actually supposed to tend to infinity.
کلیدواژه‌ها
Orthogonal functions؛ Abel's summability؛ Poisson's kernel؛ Von Karman's spectrum
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