التفاصيل البيبلوغرافية
| العنوان: |
ІНТЕГРАЛЬНІ ЗОБРАЖЕННЯ ДОДАТНО ВИЗНАЧЕНИХ ЯДЕР. (Ukrainian) |
| العنوان البديل: |
INTEGRAL REPRESENTATIONS OF POSITIVE DEFINITE KERNELS. (English) |
| المؤلفون: |
Bokhonov, Yurii E. |
| المصدر: |
System Research & Information Technologies / Sistemnì Doslìdžennâ ta Ìnformacìjnì Tehnologìï; 2023, Issue 1, p122-128, 7p |
| مصطلحات موضوعية: |
SYMMETRIC operators, PARTIAL differential equations, HILBERT space, DIFFERENTIAL operators, INTEGRAL representations, SELFADJOINT operators |
| مستخلص: |
The paper proposes proof of the possibility of an integral representation of a positive definite kernel of two pairs of variables. Using this kernel, we use the technique of constructing a new Hilbert space in which symmetric differential operators formally commute. In this case, the kernel satisfies a system of differential equations with partial derivatives. It is known that a kernel given in a subdomain of the real plane, generally speaking, does not always imply an extension to the entire plane. This possibility is related to the problem of the existence of a commuting selfadjoint extension of symmetric operators. The author applies his own results related to a commuting self-adjoint extension in a wider Hilbert space. The resulting representation in the form of an integral of elementary positive-definite kernels with respect to the spectral measure generated by the resolution of the identity of the operators allows us to extend the positive-definite kernel to the entire plane. [ABSTRACT FROM AUTHOR] |
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| قاعدة البيانات: |
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