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- Boman, Jan, 1933-
(författare)
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Local non-injectivity for weighted Radon transforms
- 2011
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Ingår i: Contemporary Mathematics. - : American Mathematical Society (AMS). - 0271-4132 .- 1098-3627. ; 559, s. 39-47
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Tidskriftsartikel (refereegranskat)abstract
- A weighted plane Radon transform $R_{\rho}$ is considered, where $\rho(x, L)$ is a smooth positive function. It is proved that the set of weight functions $\rho$, for which the map $f \mapsto R_{\rho} f$ is not locally injective, is dense in the space of smooth positive weight functions.
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| 6. |
- Crispin Quiñonez, Veronica
(författare)
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Ratliff-Rush Monomial Ideals
- 2006
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Ingår i: Contemporary Mathematics. - Providence : American Mathematical Society (AMS). - 0271-4132 .- 1098-3627. ; 423, s. 43-50
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Tidskriftsartikel (refereegranskat)
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| 7. |
- Dahlner, Anders
(författare)
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A Wiener Tauberian Theorem for weighted convolution algebras of zonal functions on the automorphism group of the unit disc
- 2006
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Ingår i: Bergman Spaces and Related Topics in Complex Analysis, Proceedings. - 0271-4132 .- 1098-3627. ; 404, s. 67-102
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Konferensbidrag (refereegranskat)abstract
- Our main result gives necessary and sufficient conditions, in terms of Fourier transforms, for an ideal in the algebra L-1(G parallel to K, omega), the convolution algebra of zonal functions on the automorphism group on the unit disc which are integrable with respect to the weight; function omega, to be dense in the algebra, or to have as closure an ideal of functions whose set of common zeros of the Fourier transforms is a finite set on the boundary of the maximal ideal space of the algebra. The weights considered behave like Legendre functions of the first kind.
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| 8. |
- Das, Pranabesh, et al.
(författare)
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Invitation to integral and rational points on curves and surfaces
- 2015
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Ingår i: Contemporary Mathematics. - Providence, Rhode Island : American Mathematical Society. - 1098-3627 .- 0271-4132. ; 654, s. 53-73
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Konferensbidrag (refereegranskat)abstract
- We provide a basic short introduction to Diophantine Geometry focusing on solutions to polynomial equations that correspond to rational and integral point of curves and surfaces. The methods employed are quite elementary and require no advanced background. We provide several explicit examples as well as ample citation for the motivated reader, aiming at introducing non-specialist to this intriguing world.
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| 10. |
- Kantor, Isaiah, et al.
(författare)
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Graded representations of graded Lie algebras and generalized representations of Jordan algebras
- 2005
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Ingår i: Noncommutative Geometry and Representation Theory in Mathematical Physics. - 1098-3627 .- 0271-4132. - 0821837184 - 9780821837184 ; 391, s. 167-174
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Konferensbidrag (refereegranskat)abstract
- We introduce and discuss a connection between representations of a certain class of graded Lie algebras and representations of Jordan algebras. This connection is stimulating in both directions. On the one hand it allows to produce an unified point of view on ordinary and Jacobson representations of Jordan algebras and formulate a notion of a generalized representation of a Jordan algebra, which includes ordinary and Jacobson representations as very special cases. The classification of irreducible generalized representations of simple Jordan algebras is given. On the other hand we prove that there are no infinite dimensional irreducible finitely graded representations of graded semisimple Lie algebras and classify the finite dimensional representations of this kind. The theorem about nonexistence of infinite dimensional irreducible finitely graded representations of graded semisimple Lie algebras has in fact as motivation the theorem about the absence of infinite dimensional irreducible representations of the semisimple finite dimensional Jordan algebra A (what is under considered connection can be formulated as the absence of 2-graded irreducible infinite dimensional representations of the 3-graded Lie algebra L(A) = U-1 circle plus U-0 circle plus U-1).
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| 13. |
- Larsson, Daniel, et al.
(författare)
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Quasi-Lie algebras
- 2005
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Ingår i: Contemporary Mathematics. - 0271-4132 .- 1098-3627. - 0821837184 ; 391, s. 241-248
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Konferensbidrag (refereegranskat)abstract
- This paper introduces a new class of algebras naturally containing, within a single framework, various deformations of the Witt, Virasoro and other Lie algebras based on twisted and deformed derivations, in addition to color Lie algebras and Lie superalgebras.
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| 14. |
- Larsson, Torbjörn, et al.
(författare)
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Ergodic convergence in subgradient optimization - with application to simplicial decomposition of convex programs
- 2012
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Ingår i: Contemporary Mathematics. - Providence, Rhode Island : American Mathematical Society. - 0271-4132 .- 1098-3627. ; 568, s. 159-186
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Tidskriftsartikel (refereegranskat)abstract
- When non-smooth, convex minimization problems are solved by subgradient optimization methods, the subgradients used will in general not accumulate to subgradients that verify the optimality of a solution obtained in the limit. It is therefore not a straightforward task to monitor the progress of subgradient methods in terms of the approximate fulfilment of optimality conditions. Further, certain supplementary information, such as convergent estimates of Lagrange multipliers and convergent lower bounds on the optimal objective value, is not directly available in subgradient schemes. As a means of overcoming these weaknesses in subgradient methods, we introduced in LPS96b, LPS96c, and LPS98 the computation of an ergodic (averaged) sequence of subgradients. Specifically, we considered a non-smooth, convex program solved by a conditional subgradient optimization scheme with divergent series step lengths, and showed that the elements of the ergodic sequence of subgradients in the limit fulfil the optimality conditions at the optimal solution, to which the sequence of iterates converges. This result has three important implications. The first is the finite identification of active constraints at the solution obtained in the limit. The second is the establishment of the convergence of ergodic sequences of Lagrange multipliers; this result enables sensitivity analyses for solutions obtained by subgradient methods. The third is the convergence of a lower bounding procedure based on an ergodic sequence of affine underestimates of the objective function; this procedure also provides a proper termination criterion for subgradient optimization methods. This article contributes first an overview of results and applications found in LPS96b, LPS96c, and LPS98 pertaining to the generation of ergodic sequences of subgradients generated within a subgradient scheme. It then presents an application of these results to that of the first instance of a simplicial decomposition algorithm for convex and non-smooth optimization problems.
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| 15. |
- Lindahl, Karl-Olof, 1975-
(författare)
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Divergence and convergence of conjugacies in non-Archimedean dynamics
- 2010
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Ingår i: Contemporary Mathematics. - Providence, RI : Amer. Math. Soc.. - 0271-4132 .- 1098-3627. ; 508, s. 89-109
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Tidskriftsartikel (refereegranskat)abstract
- We continue the study of the linearizability near an indifferent fixed point of a power series f, defined over a field of prime characteristic p. It is known since the work of Herman and Yoccoz in 1981 that Siegel’s linearization theorem is true also for non-Archimedean fields. However, they also showed that the condition in Siegel’s theorem is ‘usually’ not satisfied over fields of prime characteristic. Indeed, as proven by the author in a former paper, there exist power series f such that the associated conjugacy function diverges. We prove that if the degrees of the monomials of a power series f are divisible by p, then f is analytically linearizable. We find a lower (sometimes the best) bound of the size of the corresponding linearization disc. In the cases where we find the exact size of the linearization disc, we show, using the Weierstrass degree of the conjugacy, that f has an indifferent periodic point on the boundary. We also give a class of polynomials containing a monomial of degree prime to p, such that the conjugacy diverges.
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| 17. |
- Radnell, David, et al.
(författare)
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Quasiconformal Teichmüller theory as an analytical foundation for two dimensional conformal field theory
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Ingår i: Contemporary Mathematics. - 0271-4132 .- 1098-3627.
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Tidskriftsartikel (refereegranskat)abstract
- The functorial mathematical definition of conformal field theory was first formulated approximately 30 years ago. The underlying geometric category is based on the moduli space of Riemann surfaces with parametrized boundary components and the sewing operation. We survey the recent and careful study of these objects, which has led to significant connections with quasiconformal Teichmüller theory and geometric function theory. In particular we propose that the natural analytic setting for conformal field theory is the moduli space of Riemann surfaces with so-called Weil-Petersson class parametrizations. A collection of rigorous analytic results is advanced here as evidence. This class of parametrizations has the required regularity for CFT on one hand, and on the other hand are natural and of interest in their own right in geometric function theory.
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| 18. |
- Rosén, Andreas
(författare)
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Cauchy non-integral formulas
- 2014
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Ingår i: Contemporary Mathematics. - Providence, Rhode Island : Providence, RI; American Mathematical Society; 1999. - 9780821894330 - 9781470415259 ; 612, s. 163-178
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Konferensbidrag (refereegranskat)abstract
- We study certain generalized Cauchy integral formulas for gradients of solutions to second order divergence form elliptic systems, which appeared in recent work by P. Auscher and A. Rosen. These are constructed through functional calculus and are in general beyond the scope of singular integrals. More precisely, we establish such Cauchy formulas for solutions u with gradient in weighted spaces L-2(R-+(1+n), t(alpha) dtdx) also in the case vertical bar alpha vertical bar less than 1. In the end point cases alpha = +/- 1, we show how to apply Carleson duality results by T. Hytonen and A. Rosen to establish such Cauchy formulas.
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| 19. |
- Shahgholian, Henrik, et al.
(författare)
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Parabolic obstacle problems applied to finance
- 2007
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Ingår i: Contemporary Mathematics. - : American Mathematical Society (AMS). - 0271-4132 .- 1098-3627. ; 439, s. 117-133
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Tidskriftsartikel (refereegranskat)
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| 20. |
- Sparr, Annika, et al.
(författare)
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On the conjugate space of the Lorentz space L(phi,q)
- 2007
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Ingår i: Contemporary Mathematics. - 0271-4132 .- 1098-3627. ; 445, s. 313-336
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Konferensbidrag (refereegranskat)abstract
- Necessary and sufficient conditions are given for a Lorentz space L8phi,q) to have a trivial conjugat space. Analogous results are derived for quasi-normed spaces
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| 21. |
- Svensson, Per-Anders, 1967-
(författare)
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Criteria for non-repelling fixed points
- 2010
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Ingår i: Contemporary Mathematics. - 0271-4132 .- 1098-3627. ; , s. 239-252
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Tidskriftsartikel (refereegranskat)
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| 22. |
- Öinert, Johan
(författare)
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Simple group graded rings and maximal commutativity
- 2009
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Ingår i: Contemporary Mathematics. - 1098-3627 .- 0271-4132. - 9780821847473 ; 503, s. 159-175
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Konferensbidrag (refereegranskat)abstract
- In this paper we provide necessary and sufficient conditions for strongly group graded rings to be simple. For a strongly group graded ring R = circle plus(g is an element of G)R(g) the grading group G acts, in a natural way, as automorphisms of the comrnutant of the neutral component subring R(e) in R and of the center of R(e). We show that if R. is a strongly G-graded ring where R(e), is maximal commutative in R(e), then R is a simple ring if and only if R(e), is G-simple (i.e. there are no nontrivial G-invariant ideals). We also show that if R(e), is commutative (not necessarily maximal commutative) and the commutant of R(e)., is G-simple, then R. is a simple ring. These results apply to G-crossed products in particular. A skew group ring R(e), G, where R(e), is commutative, is shown to be a simple ring if and only if R(e), is G-simple and maximal commutative in R(e), >(sigma), G. As an interesting example we consider the skew group algebra C(X) (sic) ((h) over bar) Z associated to a topological dynamical system (X, h). We obtain necessary and sufficient conditions for simplicity of C(X) (sic) ((h) over bar) Z with respect to the dynamics of the dynamical system (X, h), but also with respect to algebraic properties of C(X) as a subalgebra of C(X) (sic) ((h) over bar) Z. Furthermore, we show that for any strongly G-graded ring R each nonzero ideal of R has a nonzero intersection with the commutant of the center of the neutral component.
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| 23. |
- Aleman, Alexandru, et al.
(författare)
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Invariant subspaces for the backward shift on Hilbert spaces of analytic functions with regular norm.
- 2006
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Ingår i: Contemporary Mathematics. - 1098-3627. ; 404, s. 1-25
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Tidskriftsartikel (refereegranskat)abstract
- It is shown that under certain regularity conditions on the norm, the functions in a nontrivial invariant subspace of the backward shift operator have meromorphic pseudocontinuations in the Nevanlinna class of the exterior of the unit disk. In addition, we provide a regularity condition which implies that the subspace itself is contained in the Nevanlinna class of the disc.
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| 25. |
- Von Rosen, Dietrich
(författare)
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On a Class of Singular Nonsymmetric Matrices with Nonnegative Integer Spectra
- 2010
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Ingår i: Contemporary Mathematics. - 0271-4132. ; 516, s. 319-324
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Konferensbidrag (refereegranskat)abstract
- This paper presents a simple derivation of eigenvalues, and left and right eigenvectors of a square nonsymmetric matrix that appears in sampling theory, and its properly normalized right eigenvectors give the inclusion probabilities. The proof is based on a special Vandermonde matrix.
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