Sarnak’s Disjointness Conjecture states that the Mobius function is disjoint with any zeroentropy flow. This note establishes this conjecture, with a rate, for Furstenberg’s irregular flows on the infinite-dimension...Sarnak’s Disjointness Conjecture states that the Mobius function is disjoint with any zeroentropy flow. This note establishes this conjecture, with a rate, for Furstenberg’s irregular flows on the infinite-dimensional torus.展开更多
In this paper, the sum of standard generalized flames of Hilbert W^＊-module is studied intensively by using operator-theoretic-methods, and some conditions are given to assure that the sum of two or more standard gen...In this paper, the sum of standard generalized flames of Hilbert W^＊-module is studied intensively by using operator-theoretic-methods, and some conditions are given to assure that the sum of two or more standard generalized frames is a standard generalized frame.展开更多
We prove the M?bius disjointness conjecture in short intervals for a class of skew products on the 2-torus,which includes Furstenberg’s example of irregular flows.
文摘Sarnak’s Disjointness Conjecture states that the Mobius function is disjoint with any zeroentropy flow. This note establishes this conjecture, with a rate, for Furstenberg’s irregular flows on the infinite-dimensional torus.
基金the National Natural Science Foundation of China （No. 10771101） and Chuangxin Funds of Nanjing University of Aeronautics and Astronautics （No. 987561）.
文摘In this paper, the sum of standard generalized flames of Hilbert W^＊-module is studied intensively by using operator-theoretic-methods, and some conditions are given to assure that the sum of two or more standard generalized frames is a standard generalized frame.
基金Supported by the National Key Reserarch and Development Program of China (Grant No.2021YFA1000700)。
文摘We prove the M?bius disjointness conjecture in short intervals for a class of skew products on the 2-torus,which includes Furstenberg’s example of irregular flows.
