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This chapter studies homogeneous operatorsHomogeneous operatorOperator and functionalsFunctional in Banach and Hilbert spacesHilbert space. Euler homogeneous functionFunction theoremHomogeneous function theorem is extended to homogeneous mappingsMapping in abstract spaces. A characterization of homogeneous linear operatorOperator in a Banach spaceBanach space  is presented. The concept of homogeneous extension of an infinite-dimensional operatorOperator is introduced. Examples of various homogeneous operatorsHomogeneous operator are presented.

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Infinite-Dimensional Homogeneous Mappings

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  • 发表日期：

    2025年

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  • Andrey Polyakov

摘要

This chapter studies homogeneous operatorsHomogeneous operatorOperator and functionalsFunctional in Banach and Hilbert spacesHilbert space. Euler homogeneous functionFunction theoremHomogeneous function theorem is extended to homogeneous mappingsMapping in abstract spaces. A characterization of homogeneous linear operatorOperator in a Banach spaceBanach space  is presented. The concept of homogeneous extension of an infinite-dimensional operatorOperator is introduced. Examples of various homogeneous operatorsHomogeneous operator are presented.