کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9502986 | 1339551 | 2005 | 16 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Differential equations in spaces of compact operators
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We study a system of differential equations in C(H), the space of all compact operators on a separable complex Hilbert space, H. The systems considered are infinite-dimensional generalizations of mathematical models of learning, implementable as artificial neural networks. In this new setting, in addition to the usual questions of existence and uniqueness of solutions, we discuss issues which are operator theoretic in nature. Under some restrictions on the initial condition, we explicitly solve the system and represent the solution in terms of the spectral representation of the initial condition. We also discuss the stability of those solutions, and describe the weak, strong, and uniform limit sets in terms of their respective spectral properties.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 308, Issue 1, 1 August 2005, Pages 105-120
Journal: Journal of Mathematical Analysis and Applications - Volume 308, Issue 1, 1 August 2005, Pages 105-120
نویسندگان
Fernanda Botelho, James E. Jamison,