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Titlebook: Operational Calculus; A Theory of Hyperfun K. Yosida Book 1984 Springer Science+Business Media New York 1984 Derivative.Finite.Hyperfunktio

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發(fā)表于 2025-3-21 16:57:03 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Operational Calculus
副標(biāo)題A Theory of Hyperfun
編輯K. Yosida
視頻videohttp://file.papertrans.cn/702/701999/701999.mp4
叢書名稱Applied Mathematical Sciences
圖書封面Titlebook: Operational Calculus; A Theory of Hyperfun K. Yosida Book 1984 Springer Science+Business Media New York 1984 Derivative.Finite.Hyperfunktio
描述In the end of the last century, Oliver Heaviside inaugurated an operational calculus in connection with his researches in electromagnetic theory. In his operational calculus, the operator of differentiation was denoted by the symbol "p". The explanation of this operator p as given by him was difficult to understand and to use, and the range of the valid- ity of his calculus remains unclear still now, although it was widely noticed that his calculus gives correct results in general. In the 1930s, Gustav Doetsch and many other mathematicians began to strive for the mathematical foundation of Heaviside‘s operational calculus by virtue of the Laplace transform -pt e f(t)dt. ( However, the use of such integrals naturally confronts restrictions con- cerning the growth behavior of the numerical function f(t) as t ~ ~. At about the midcentury, Jan Mikusinski invented the theory of con- volution quotients, based upon the Titchmarsh convolution theorem: If f(t) and get) are continuous functions defined on [O,~) such that the convolution f~ f(t-u)g(u)du =0, then either f(t) =0 or get) =0 must hold. The convolution quotients include the operator of differentiation "s" and related operators. Mi
出版日期Book 1984
關(guān)鍵詞Derivative; Finite; Hyperfunktion; Identity; Operatorenrechnung; algebra; calculus; differential equation; e
版次1
doihttps://doi.org/10.1007/978-1-4612-1118-1
isbn_softcover978-0-387-96047-0
isbn_ebook978-1-4612-1118-1Series ISSN 0066-5452 Series E-ISSN 2196-968X
issn_series 0066-5452
copyrightSpringer Science+Business Media New York 1984
The information of publication is updating

書目名稱Operational Calculus影響因子(影響力)




書目名稱Operational Calculus影響因子(影響力)學(xué)科排名




書目名稱Operational Calculus網(wǎng)絡(luò)公開度




書目名稱Operational Calculus網(wǎng)絡(luò)公開度學(xué)科排名




書目名稱Operational Calculus被引頻次




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沙發(fā)
發(fā)表于 2025-3-21 23:55:27 | 只看該作者
板凳
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Introduction of the Operator h Through the Convolution Ring Ce in the .; we shall denote the class of those functions by C[0,∞) or simply by the letter C. The convolution of two functions a = a(t) and b = b(t) of . is defined by . and we have PROPOSITION 1. a*b belongs to .; i.e., a*b(t) is a continuous function defined on [0, ∞).
地板
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5#
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Heat Equationdenote the ., c the ., and ρ the . of the bar. Furthermore, let the lateral surface of the bar be perfectly insulated so that heat can flow in and flow out only through the ends of the bar. If we denote by z(λ,t) the temperature at the point of the bar at abcissa λ at the instant t, then the heat equation in the bar is
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發(fā)表于 2025-3-23 00:26:23 | 只看該作者
Introduction of the Operator s Through the Ring CHLet ..then,for any k = h.∈H and f ∈c,we have ..
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發(fā)表于 2025-3-23 05:11:42 | 只看該作者
10#
發(fā)表于 2025-3-23 05:40:00 | 只看該作者
Fractional Powers of Hyperfunctions h, s and These functions are respectively defined by Euler’s* integrals:
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