共查询到20条相似文献,搜索用时 31 毫秒
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《Comptes Rendus Mathematique》2014,352(7-8):577-581
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This text is a report on work progress. We introduce the class of cyclotomic model sets (mathematical quasicrystals) , where is the ring of integers in the nth cyclotomic field , and discuss the corresponding decomposition, consistency and reconstruction problems of the discrete tomography of these sets. Our solution of the so-called decomposition problem also applies to the case of the square lattice , which corresponds to the classical setting of discrete tomography. 相似文献
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Using the Unified Transform, also known as the Fokas method, the solution of the sine-Gordon equation in the quarter plane can be expressed in terms of the solution of a matrix Riemann–Hilbert problem whose definition involves four spectral functions . The functions and are defined via a nonlinear Fourier transform of the initial data, whereas and are defined via a nonlinear Fourier transform of the boundary values. In this paper, we provide an extensive study of these nonlinear Fourier transforms and the associated eigenfunctions under weak regularity and decay assumptions on the initial and boundary values. The results can be used to determine the long-time asymptotics of the sine-Gordon quarter-plane solution via nonlinear steepest descent techniques. 相似文献
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We give a characterization, in one variable case, of those multipliers F such that the division problem is solvable in . For these functions we even prove that the multiplication operator has a continuous linear right inverse on , in contrast to what happens in the several variables case, as was shown by Langenbruch. 相似文献
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Vladimir Shchigolev 《Journal of Algebra》2009,321(5):1453-1462
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Abhishek Banerjee 《Comptes Rendus Mathematique》2018,356(4):365-375
Let be the spectrum of a tensor-triangulated category . We show that there is a homeomorphism between the spectral space of radical thick tensor ideals in and the collection of open subsets of in inverse topology. In fact, we prove a more general result in terms of supports on and work by combining methods from commutative algebra, topology and tensor triangular geometry. 相似文献
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Maxim Gurevich 《Journal of Functional Analysis》2012,262(10):4270-4301
We develop the theory of subproduct systems over the monoid , and the non-self-adjoint operator algebras associated with them. These are double sequences of Hilbert spaces equipped with a multiplication given by coisometries from to . We find that the character space of the norm-closed algebra generated by left multiplication operators (the tensor algebra) is homeomorphic to a complex homogeneous affine algebraic variety intersected with a unit ball. Certain conditions are isolated under which subproduct systems whose tensor algebras are isomorphic must be isomorphic themselves. In the absence of these conditions, we show that two numerical invariants must agree on such subproduct systems. Additionally, we classify the subproduct systems over by means of ideals in algebras of non-commutative polynomials. 相似文献
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Dana Bartošová Jordi Lopez-Abad Martino Lupini Brice Mbombo 《Comptes Rendus Mathematique》2017,355(12):1242-1246
We show that the class of finite-dimensional Banach spaces and the class of finite-dimensional Choquet simplices have the Ramsey property. As an application, we show that the group of surjective linear isometries of the Gurarij space is extremely amenable, and that the canonical action is the universal minimal flow of the group of affine homeomorphisms of the Poulsen simplex . This answers questions of Melleray–Tsankov and Conley–Törnquist. 相似文献
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In this paper, we consider the function field analogue of the Lehmer's totient problem. Let and be the Euler's totient function of over , where is a finite field with q elements. We prove that if and only if (i) is irreducible; or (ii) , is the product of any 2 non-associate irreducibles of degree 1; or (iii) , is the product of all irreducibles of degree 1, all irreducibles of degree 1 and 2, and the product of any 3 irreducibles one each of degree 1, 2 and 3. 相似文献