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- W3203563254 abstract "The article studies some characteristic properties of self-adjoint partially integral operators of Fredholm type in the Kaplansky-Hilbert module $L_{0}left[L_{2}left(Omega_{1}right)right]$ over $L_{0}left(Omega_{2}right)$. Some mathematical tools from the theory of Kaplansky-Hilbert module are used. In the Kaplansky-Hilbert module $L_{0}left[L_{2}left(Omega_{1}right)right]$ over $ L_{0} left (Omega _ {2} right)$ we consider the partially integral operator of Fredholm type $T_{1}$ ($ Omega_{1} $ and $Omega_{2} $ are closed bounded sets in $ {mathbb R}^{nu_{1}}$ and $ {mathbb R}^{nu_{2}},$ $nu_{1}, nu_{2} in {mathbb N} $, respectively). The existence of $ L_{0} left (Omega _ {2} right) $ nonzero eigenvalues for any self-adjoint partially integral operator $T_{1}$ is proved; moreover, it is shown that $T_{1}$ has finite and countable number of real $L_{0}(Omega_{2})$-eigenvalues. In the latter case, the sequence $ L_{0}(Omega_{2})$-eigenvalues is order convergent to the zero function. It is also established that the operator $T_{1}$ admits an expansion into a series of $nabla_{1}$-one-dimensional operators." @default.
- W3203563254 created "2021-10-11" @default.
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- W3203563254 date "2021-09-23" @default.
- W3203563254 modified "2023-10-17" @default.
- W3203563254 title "Partial integral operators of Fredholm type on Kaplansky-Hilbert module over $L_0$" @default.
- W3203563254 cites W2035725604 @default.
- W3203563254 doi "https://doi.org/10.46698/w5172-0182-0041-c" @default.
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