Geodesic
On the stricture of normal Hausdorff operators on Lebesgue spaces
Funkcionalʹnyj analiz i ego priloženiâ, Tome 53 (2019) no. 4, pp. 27-37

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We consider a generalization of Hausdorff operator and introduce the notion of the symbol of such an operator. Using this notion we describe under some natural conditions the structure and investigate important properties (such as invertibility, spectrum, norm, and compactness) of normal generalized Hausdorff operators on Lebesgue spaces over $\mathbb{R}^n.$ The examples of Cesàro operators are considered.
Keywords: Hausdorff operator, Cesàro operator, symbol of an operator, normal operator, spectrum, compact operator. 
@article{FAA_2019_53_4_a2,
     author = {A. R. Mirotin},
     title = {On the stricture of normal {Hausdorff} operators on {Lebesgue} spaces},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {27--37},
     publisher = {mathdoc},
     volume = {53},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2019_53_4_a2/}
}
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A. R. Mirotin. On the stricture of normal Hausdorff operators on Lebesgue spaces. Funkcionalʹnyj analiz i ego priloženiâ, Tome 53 (2019) no. 4, pp. 27-37. http://geodesic.mathdoc.fr/item/FAA_2019_53_4_a2/