作者: gimmick 時間: 2025-3-21 22:01 作者: 類型 時間: 2025-3-22 03:18
Basic Hyperfunctions,rentiation and definite integration. Then, not only almost all familiar functions, but also objects such as the δ-function, can be reinterpreted as hyperfunctions and dealt with in a unified way. In this chapter we discuss, in detail, several examples of basic hyperfunctions. We begin with character作者: CARE 時間: 2025-3-22 04:33 作者: ABIDE 時間: 2025-3-22 12:24
Fourier Transformation, Thus, we now have a basis on which we can perform differentiation and integration of hyperfunctions without obstacles. In the present chapter, we start the theory of Fourier transformations of hyperfunctions. In physical sciences and engineering, some problems are conveniently dealt with by Fourier作者: 馬籠頭 時間: 2025-3-22 15:43 作者: Stress 時間: 2025-3-22 18:20 作者: 發(fā)展 時間: 2025-3-22 23:00
Fourier Transforms-Existence and Regularity,main of functions (hyperfunctions) e.g. .1 = δ(.), .. = -..δ(ξ), .(1/x) = -π.sgnξ, .... The Fourier transform .(ξ) = ..(.) of a hyperfunction .(.) = H. F. .(.) is defined by .. (Definition 5.1.) Contours . and . of (1.2) consist of two semi-infinite curves each as shown in Figure 1. Whenever the int作者: 十字架 時間: 2025-3-23 03:42
Fourier Transform-Asymptotic Behaviour,) may or may not be expressed in a closed form, i.e. in terms of known functions. In such a case we have to return to the definition of Fourier transformation and calculate numerically the infinite integral .. If ξ is not very large, numerical integration can be performed relatively easily, but for 作者: Expurgate 時間: 2025-3-23 07:51 作者: Atmosphere 時間: 2025-3-23 13:14 作者: Etymology 時間: 2025-3-23 17:01
Product of Hyperfunctions,tion, multiplication and division, the first two are, of course, possible as linear combinations. There are, however, problems with multiplication and division. It may even seem meaningless to consider products of hyperfunctions in a theory such as the Schwartz distribution theory which is based on 作者: 抗生素 時間: 2025-3-23 21:11 作者: septicemia 時間: 2025-3-24 00:16
Hilbert Transforms and Conjugate Hyperfunctions,t chapter is to treat them in a unified way from the viewpoint of hyperfunction theory. It will be seen that Hilbert transformation is just the same as convolution with the hyperfunction 1/. and the conjugate Fourier series is the Hilbert transform of a periodic hyperfunction (i.e. Fourier series). 作者: Spartan 時間: 2025-3-24 04:29
Poisson-Schwarz Integral Formulae,its normal derivative δФ/δn assumes specified values on the boundary. Many problems of physics and engineering can be reduced to this problem. In two-dimensional problems, an equivalent is to find an analytic function . regular in D such that Re . or Im . assumes specified values on the boundary. Wh作者: 搜集 時間: 2025-3-24 09:30 作者: 壁畫 時間: 2025-3-24 14:40
Laplace Transforms,m is worked out for hyperfunctions, the theory will have much broader applicability than it has for ordinary functions. However, we need not deal with the Laplace transform .. We can deal with it as a variant representation of the Fourier transform in the framework of the theory of the Fourier trans作者: Herd-Immunity 時間: 2025-3-24 18:29 作者: indecipherable 時間: 2025-3-24 22:56
Xiaoxu Li,Marcel Wira,Ruck Thawonmasd side represents ‘something’ determined by a pair of analytic functions: ..(.), F.-(.) , and write .. We call this ‘something‘ a .. To save space, it may be written [F.(.), F.(.)]. Alternatively, we may write the pair ..(.), .-(.) simply as .(.), so that (1.2) becomes: .(.)→.(.). (1.3)作者: obnoxious 時間: 2025-3-25 02:08 作者: 卡死偷電 時間: 2025-3-25 03:27 作者: certain 時間: 2025-3-25 10:42 作者: frivolous 時間: 2025-3-25 12:16
Thorsten Hennig-Thurau,Mark B. Houstonution of periodic hyperfunctions, it would be useful to view infinite integrals, arising in the definition of convolution, as infinite principal-value integrals. In fact, if such a revision is done, the domain of application of convolution is very much extended.作者: Orgasm 時間: 2025-3-25 17:54
Thorsten Hennig-Thurau,Mark B. HoustonTherefore, the content of this chapter can be regarded as an application of Chapters 13 and 14. Since the Poisson-Schwarz integration formula of complex function theory will be discussed from the viewpoint of hyperfunction theory, we also derive several formulae on which the Poisson-Schwarz formula is based.作者: 專心 時間: 2025-3-25 23:44
Pilar Lacasa,Laura Méndez,Sara Cortésen D is a circle or a halfplane, formulae to express the solution are known and are called the .. In this chapter, we discuss these formulae and related facts from the viewpoint of hyperfunction theory. As an example of their application we deal with integral equations related to the Hilbert transforms.作者: regale 時間: 2025-3-26 03:00
Book 1992 for non-specialists. To remedy thissituation, this book gives an intelligible exposition of generalizedfunctions based on Sato‘s hyperfunction, which is essentially the`boundary value of analytic functions‘. An intuitive image --hyperfunction = vortex layer -- is adopted, and only an elementaryknow作者: 薄荷醇 時間: 2025-3-26 04:29
0924-4913 accessible for non-specialists. To remedy thissituation, this book gives an intelligible exposition of generalizedfunctions based on Sato‘s hyperfunction, which is essentially the`boundary value of analytic functions‘. An intuitive image --hyperfunction = vortex layer -- is adopted, and only an elem作者: chuckle 時間: 2025-3-26 10:56
Entertainment Computing – ICEC 2022perfunctions and dealt with in a unified way. In this chapter we discuss, in detail, several examples of basic hyperfunctions. We begin with characteristics of individual hyperfunctions such as ., etc.作者: intercede 時間: 2025-3-26 14:38 作者: amyloid 時間: 2025-3-26 18:37
Nicolas Grelier,Stéphane Kaufmann. F. .(.) is defined by .. (Definition 5.1.) Contours . and . of (1.2) consist of two semi-infinite curves each as shown in Figure 1. Whenever the integral of (1.2) exists, the Fourier transform .(ζ) of .(.) exists.作者: 教育學(xué) 時間: 2025-3-26 22:10
The Meaning of Life (in Video Games)ormation and calculate numerically the infinite integral .. If ξ is not very large, numerical integration can be performed relatively easily, but for large ξ the integrand oscillates so rapidly that numerical integration would be impracticable.作者: 口訣法 時間: 2025-3-27 03:04 作者: 音樂等 時間: 2025-3-27 05:29
Lecture Notes in Computer Scienceressure of the obligation to produce periodical instalments, the framework of my plan was gradually developed. To show how my plan changed during the time, I am including the “Concluding remarks” of the last instalment.作者: Immunotherapy 時間: 2025-3-27 11:45
Basic Hyperfunctions,perfunctions and dealt with in a unified way. In this chapter we discuss, in detail, several examples of basic hyperfunctions. We begin with characteristics of individual hyperfunctions such as ., etc.作者: 預(yù)測 時間: 2025-3-27 14:18 作者: 泥土謙卑 時間: 2025-3-27 20:48 作者: SLUMP 時間: 2025-3-27 22:43
Fourier Transform-Asymptotic Behaviour,ormation and calculate numerically the infinite integral .. If ξ is not very large, numerical integration can be performed relatively easily, but for large ξ the integrand oscillates so rapidly that numerical integration would be impracticable.作者: VAN 時間: 2025-3-28 04:00 作者: Ledger 時間: 2025-3-28 09:19 作者: STERN 時間: 2025-3-28 13:57
Operations on Hyperfunctions,d side represents ‘something’ determined by a pair of analytic functions: ..(.), F.-(.) , and write .. We call this ‘something‘ a .. To save space, it may be written [F.(.), F.(.)]. Alternatively, we may write the pair ..(.), .-(.) simply as .(.), so that (1.2) becomes: .(.)→.(.). (1.3)作者: Indict 時間: 2025-3-28 15:03 作者: LATHE 時間: 2025-3-28 22:19
Fourier Transformation of Power-Type Hyperfunctions, as ordinary functions. However, as will be seen later, these power-type hyperfunctions play decisive roles when we investigate the asymptotic behaviour of the Fourier transforms .(ξ) = ..(.) for ξ → ∞ for a given function . (.).作者: Generic-Drug 時間: 2025-3-29 01:35 作者: Dysplasia 時間: 2025-3-29 04:21 作者: 是貪求 時間: 2025-3-29 07:45 作者: lymphoma 時間: 2025-3-29 12:53
Poisson-Schwarz Integral Formulae,en D is a circle or a halfplane, formulae to express the solution are known and are called the .. In this chapter, we discuss these formulae and related facts from the viewpoint of hyperfunction theory. As an example of their application we deal with integral equations related to the Hilbert transforms.作者: 慢跑鞋 時間: 2025-3-29 18:35
Miriam-Linnea Hale,André Melzert . = O. Therefore, ..(.) and ..(.) are simpler than .(.) itself, so that it may be convenient to consider hyperfunctions corresponding to .. (.) and ..(.) and to combine them to obtain the hyperfunction corresponding to .(.).作者: 客觀 時間: 2025-3-29 21:09 作者: fiscal 時間: 2025-3-30 01:10 作者: 首創(chuàng)精神 時間: 2025-3-30 05:41
Periodic Hyperfunctions and Fourier Series Fourier Series,his chapter we study periodic hyperfunctions. Then we shall see that the theory of Fourier series is naturally absorbed into the theory of Fourier transformations. For this purpose, we shall first introduce the concept of standard generating functions.作者: 知道 時間: 2025-3-30 09:58
Integral Equations, were taken up as examples. Since the aim was to show applications of Hilbert transforms, we considered only integral equations of very special types. In this chapter, we choose examples of integral equations from a wider domain and explain how to deal with them using hyperfunction theory.作者: 刪除 時間: 2025-3-30 14:09 作者: Canyon 時間: 2025-3-30 19:25 作者: 受人支配 時間: 2025-3-30 22:15 作者: 玉米 時間: 2025-3-31 03:37 作者: NAG 時間: 2025-3-31 07:37
Mathematics and its Applicationshttp://image.papertrans.cn/a/image/159862.jpg作者: 生氣地 時間: 2025-3-31 13:16
Thorsten Hennig-Thurau,Mark B. HoustonLet us begin with two ordinary functions ..(.) and ..(.) and suppose that their Fourier transforms . exist. The Fourier transform of the product ..(.) · ..(.) is . Since ..(.) is the inverse Fourier transform of ψ(ξ), we have . Substituting this into the r.h.s. of (1.2) gives..作者: Cumbersome 時間: 2025-3-31 14:34 作者: 發(fā)源 時間: 2025-3-31 20:55 作者: Hyaluronic-Acid 時間: 2025-3-31 22:02 作者: 河潭 時間: 2025-4-1 05:15
Entertainment Computing – ICEC 2022rentiation and definite integration. Then, not only almost all familiar functions, but also objects such as the δ-function, can be reinterpreted as hyperfunctions and dealt with in a unified way. In this chapter we discuss, in detail, several examples of basic hyperfunctions. We begin with character作者: Debility 時間: 2025-4-1 07:45
https://doi.org/10.1007/978-3-031-20212-4ositive integers). The concept of a formal product, i.e. hyperfunctions of the form . with a hyperfunction . and a single-valued analytic function ., played a basic role. Moreover, hyperfunctions ∣.∣., ∣.∣.H(.), ∣.∣. sgn . etc. were defined for α complex. What are the relations between them and .. ,作者: 類人猿 時間: 2025-4-1 10:29
Entertainment Computing – ICEC 2022 Thus, we now have a basis on which we can perform differentiation and integration of hyperfunctions without obstacles. In the present chapter, we start the theory of Fourier transformations of hyperfunctions. In physical sciences and engineering, some problems are conveniently dealt with by Fourier作者: 不確定 時間: 2025-4-1 15:25 作者: BUST 時間: 2025-4-1 20:18
