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The connection between geodesics on the modular surface and regular continued fractions, established by Series, is extended to a connection between geodesics on
and odd and grotesque continued fractions, where is the index two subgroup of generated by the order three elements and , and having an ideal quadrilateral as fundamental domain.A similar connection between geodesics on
and even continued fractions is discussed in our framework, where denotes the Theta subgroup of generated by and . 相似文献
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Hyoung Joon Kim 《Journal of Mathematical Analysis and Applications》2012,386(1):110-114
It is well known that if , where A is compact, then T has a nontrivial hyperinvariant subspace. In this paper, we try to solve the hyperinvariant subspace problem for operators which have a compact part. Our main result is that if A is compact, then either or has a nontrivial hyperinvariant subspace. 相似文献
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We prove the so-called conjecture: for every real-monic polynomial of degree there exists an n by n matrix with sign patternwhose characteristic polynomial is . The proof converts the problem of determining the nonsingularity of a certain Jacobi matrix to the problem of proving the non-existence of a nonzero matrix B that commutes with a nilpotent matrix with sign pattern and has zeros in positions , and for . 相似文献
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One dimensional Dirac operators considered with -potentials and subject to regular boundary conditions (), have discrete spectrum. For strictly regular , the spectrum of the free operator is simple while the spectrum of is eventually simple, and the corresponding normalized root function systems are Riesz bases. For expansions of functions of bounded variation about these Riesz bases, we prove the uniform equiconvergence property and point-wise convergence on the closed interval . Analogous results are obtained for regular but not strictly regular . 相似文献
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