Measure-compact operators, almost compact operators, and linear functional equations in L p
- 48 Downloads
Under study are the measure-compact operators and almost compact operators in L p . We construct an example of a measure-compact operator that is not almost compact. Introducing two classes of closed linear operators in L p , we prove that the resolvents of these operators are almost compact or measure-compact. We present methods for the reduction of linear functional equations of the second kind in L p with almost compact or measure-compact operators to equivalent linear integral equations in L p with quasidegenerate Carleman kernels.
Keywordsalmost compact operator measure-compact operator integral operator Carleman operator linear functional equation of the second kind in Lp linear integral equations in Lp
Unable to display preview. Download preview PDF.
- 3.Kashin B. S. and Saakyan A. A., Orthogonal Series [in Russian], AFTs, Moscow (1999).Google Scholar
- 6.Korotkov V. B., Integral Operators [in Russian], Nauka, Novosibirsk (1983).Google Scholar
- 8.Sobolev S. L., Introduction to the Theory of Cubature Formulas, Gordon and Breach Science Publishers, Montreux (1974).Google Scholar
- 10.Korotkov V. B., Some Topics in the Theory of Integral Operators [in Russian], Inst. Mat., Novosibirsk (1988).Google Scholar
- 11.Pietsch A., Operator Ideals, VEB Deutscher Verlag der Wissenschaften, Berlin (1978).Google Scholar
- 12.Korotkov V. B., Integral Operators with Carleman-Type Kernels [in Russian], Diss. Dokt. Fiz.-Mat. Nauk, Inst. Mat., Novosibirsk (1971).Google Scholar