A general approach to transference principles for discrete and continuous sequence of operators (semi) groups is described. This allows one to recover the classical transference results of Calderon, Coifman and Weiss ...A general approach to transference principles for discrete and continuous sequence of operators (semi) groups is described. This allows one to recover the classical transference results of Calderon, Coifman and Weiss and of Berkson, Gilleppie and Muhly and the more recent one of the author. The method is applied to derive a new transference principle for (discrete and continuous) the sequence of operators semigroups that need not be grouped. As an application, functional calculus estimates for bounded sequence of operators with at most polynomially growing powers are derived, leading to a new proof of classical results by Peller from 1982. The method allows for a generalization of his results away from Hilbert spaces to -spaces and—involving the concept of γ-boundedness—to general spaces. Analogous results for strongly-continuous one-parameter (semi) groups are presented as well by Markus Haase [1]. Finally, an application is given to singular integrals for one-parameter semigroups.展开更多
Non-recursive relations structure-functionality is an exclusive property of the recently introduced concept of boundedness. They provide a leading role of the hierarchy of the functional organization in the evolution ...Non-recursive relations structure-functionality is an exclusive property of the recently introduced concept of boundedness. They provide a leading role of the hierarchy of the functional organization in the evolution of each and every complex system. The novel evolution strategy appears as a counterpart rather than as opponent to the survival of the fittest strategy because the survival of the fittest is more advantageous strategy in a slow varying environment while the novel strategy is more advantageous for a rapidly changing environment. Alongside, the non-recursive relations structure-functionality serves as grounds for coexistence of scaling dependent and scaling independent properties of complex systems.展开更多
文摘A general approach to transference principles for discrete and continuous sequence of operators (semi) groups is described. This allows one to recover the classical transference results of Calderon, Coifman and Weiss and of Berkson, Gilleppie and Muhly and the more recent one of the author. The method is applied to derive a new transference principle for (discrete and continuous) the sequence of operators semigroups that need not be grouped. As an application, functional calculus estimates for bounded sequence of operators with at most polynomially growing powers are derived, leading to a new proof of classical results by Peller from 1982. The method allows for a generalization of his results away from Hilbert spaces to -spaces and—involving the concept of γ-boundedness—to general spaces. Analogous results for strongly-continuous one-parameter (semi) groups are presented as well by Markus Haase [1]. Finally, an application is given to singular integrals for one-parameter semigroups.
文摘Non-recursive relations structure-functionality is an exclusive property of the recently introduced concept of boundedness. They provide a leading role of the hierarchy of the functional organization in the evolution of each and every complex system. The novel evolution strategy appears as a counterpart rather than as opponent to the survival of the fittest strategy because the survival of the fittest is more advantageous strategy in a slow varying environment while the novel strategy is more advantageous for a rapidly changing environment. Alongside, the non-recursive relations structure-functionality serves as grounds for coexistence of scaling dependent and scaling independent properties of complex systems.
