1,721,053 research outputs found
Finite dimensional semigroup quadratic algebras with the minimal number of relations
No full textA quadratic semigroup algebra is an algebra over a field given by the generators x_1, . . . , x_n and a finite set of quadratic relations each of which either has the shape x_j x_k = 0 or the shape x_j x_k = x_l x_m . We prove that a quadratic semigroup algebra given by n generators and d=(n^2+n)/4 relations is always infinite dimensional. This strengthens the Golod–Shafarevich estimate for the above class of algebras. Our main result however is that for every n, there is a finite dimensional quadratic semigroup algebra with n generators and d_n relations, where d_n is the first integer greater than (n^2+n)/4 . That is, the above Golod–Shafarevich-type estimate for semigroup algebras is sharp
Non-sequential weak supercyclicity and hypercyclicity
No full textAbstractA bounded linear operator T acting on a Banach space B is called weakly hypercyclic if there exists x∈B such that the orbit {Tnx:n=0,1,…} is weakly dense in B and T is called weakly supercyclic if there is x∈B for which the projective orbit {λTnx:λ∈C,n=0,1,…} is weakly dense in B. If weak density is replaced by weak sequential density, then T is said to be weakly sequentially hypercyclic or supercyclic, respectively. It is shown that on a separable Hilbert space there are weakly supercyclic operators which are not weakly sequentially supercyclic. This is achieved by constructing a Borel probability measure μ on the unit circle for which the Fourier coefficients vanish at infinity and the multiplication operator Mf(z)=zf(z) acting on L2(μ) is weakly supercyclic. It is not weakly sequentially supercyclic, since the projective orbit under M of each element in L2(μ) is weakly sequentially closed. This answers a question posed by Bayart and Matheron. It is proved that the bilateral shift on ℓp(Z), 1⩽p<∞, is weakly supercyclic if and only if 2<p<∞ and that any weakly supercyclic weighted bilateral shift on ℓp(Z) for 1⩽p⩽2 is norm supercyclic. It is also shown that any weakly hypercyclic weighted bilateral shift on ℓp(Z) for 1⩽p<2 is norm hypercyclic, which answers a question of Chan and Sanders
On the Gelʹfand-Dikiĭ method for computing the first eigenvalues of the Sturm-Liouville operator
No full textThree constructive examples of separable pre-Hilbert spaces nonisomorphic to their closed hyperplanes
No full textAn example of a sigma -compact infinite-dimensional pre-Hilbert space H is constructed such that any continuous linear operator T: H --> H is of the form T = lambdaI + F for some lambda is an element of R and for a finite-dimensional continuous linear operator F. A class of simple examples of pre-Hilbert spaces nonisomorphic to their closed hyperplanes is given. A sigma -compact pre-Hilbert space H isomorphic to H x R x R and nonisomorphic to H x R is also constructed
The spectrum of the Liouville-von Neumann operator in the Hilbert-Schmidt space
No full textThe singular continuous spectrum of the Liouville operator of quantum statistical physics is, in general, properly included in the difference of the spectral values of the singular continuous spectrum of the associated Hamiltonian. The absolutely continuous spectrum of the Liouvillian may arise from a purely singular continuous Hamiltonian. We provide the correct formulas for the spectrum of the Liouville operator and show that the decaying states of the singular continuous subspace of the Hamiltonian do not necessarily contribute to the absolutely continuous subspace of the Liouvillian
On the spectrum of frequently hypercyclic operators
Get PDFA bounded linear operator T on a Banach space X is called frequently hypercyclic if there exists x ∈ X such that the lower density of the set { n ∈ N : Tnx ∈ U } is positive for any non-empty open subset U of X. Bayart and Grivaux have raised a question whether there is a frequently hypercyclic operator on any separable infinite dimensional Banach space. We prove that the spectrum of a frequently hypercyclic operator has no isolated points. It follows that there are no frequently hypercyclic operators on all complex and on some real hereditarily indecomposable Banach spaces, which provides a negative answer to the above question.<br/
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Extended spectral decompositions of the Renyi map
No full textWe present new general methods to obtain spectral decompositions of dynamical systems in rigged Hilbert spaces and investigate the existence of resonances and the completeness of the associated eigenfunctions. The results are illustrated explicitly for the simplest chaotic endomorphism, namely the Renyi map
- …
