Một vài ứng dụng của toán tử giả vi phân giải tích

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Tác giả: Sỹ Anh Tuấn Nguyễn

Ngôn ngữ: Vie

Ký hiệu phân loại: 510 Mathematics

Thông tin xuất bản: Tạp chí Khoa học Giao thông vận tải 2022

Mô tả vật lý: 502-513

Bộ sưu tập: Metadata

ID: 395524

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Lý thuyết toán tử giả vi phân giải tích là một phần mở rộng của toán tử vi phân, là một công cụ mạnh để nghiên cứu ứng dụng của Giải tích Fourier vào phương trình đạo hàm riêng. Bài báo này nghiên cứu một vài ứng dụng sâu sắc của toán tử giả vi phân giải tích đã và đang được một số nhà toán học quan tâm. Không gian các hàm nguyên exponent type bé hơn R và đại số các toán tử giả vi phân giải tích trên không gian này được đưa vào ở Phần 2 của bài báo. Tiêu chuẩn để nhận biết một hàm thuộc không gian các hàm nguyên exponent type bé hơn R được phát biểu và chứng minh ở Mệnh đề 2.1. Ở Phần 3 của bài báo trình bày một ứng dụng của toán tử giả vi phân giải tích với ký hiệu là hàm sinh exponent của dãy số Bernoulli mở rộng để nghiên cứu nghiệm của phương trình sai phân (5) được đưa vào ở Phần 3. Toán tử tích chập là một toán tử giả vi phân giải tích được sử dụng một cách khéo léo vào bài toán biến đổi Laplace ngược trên không gian Hilbert tách được được đưa vào ở phần cuối của bài báo., Tóm tắt tiếng anh, The theory of analytic pseudo-differential operators is an extension of differential operators, which is a powerful tool to study the application of Fourier analysis to partial differential equations. This paper studies some profound applications of the analytic pseudo- differential operator that has been of interest to some mathematicians. The space of entire functions of exponential type is less than R and the algebra of pseudo-differential analytic operators on this space are included in Part 2 of the paper. The criterion for identifying a function in the space of exponent entire functions of type less than R is stated and proven in Proposition 2.1. In Part 3 of the paper, an application of the analytic pseudo-differential operator is presented, denoted as the exponent generator function of the extended Bernoulli series of numbers, is presented to study the solution of differential equations, where the shift operator and, the constant is the polynomial of the difference (5) introduced in Part 3. The convolution operator is an analytic pseudo-differential operator cleverly used in the inverse Laplace transform problem in the separable Hilbert spaces included at the end of the paper.

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