2,527 research outputs found
Dynamics and spectrum of the Cesà ro operator on C-infinity(R+)
[EN] The spectrum and point spectrum of the Cesaro averaging operator C acting on the Frechet space C-infinity(R+) of all C-infinity functions on the interval [0, infinity) are determined. We employ an approach via C-0-semigroup theory for linear operators. A spectral mapping theorem for the resolvent of a closed operator acting on a locally convex space is established; it constitutes a useful tool needed to establish the main result. The dynamical behaviour of C is also investigated.The research of the first two authors was partially supported by the projects MTM2013-43540-P, GVA Prometeo II/2013/013 and GVA ACOMP/2015/186 (Spain).Albanese, AA.; Bonet Solves, JA.; Ricker, WJ. (2016). Dynamics and spectrum of the Cesà ro operator on C-infinity(R+). Monatshefte für Mathematik. 181:267-283. https://doi.org/10.1007/s00605-015-0863-zS267283181Albanese, A.A., Bonet, J., Ricker, W.J.: Mean ergodic operators in Fréchet spaces. Ann. Acad. Sci. Fenn. Math. 34, 401–436 (2009)Albanese, A.A., Bonet, J., Ricker, W.J.: Mean ergodic semigroups of operators. Rev. R. Acad. Cien. Serie A Mat. RACSAM 106, 299–319 (2012)Albanese, A.A., Bonet, J., Ricker, W.J.: Montel resolvents and uniformly mean ergodic semigroups of linear operators. Quaest. Math. 36, 253–290 (2013)Albanese, A.A., Bonet, J., Ricker, W.J.: Convergence of arithmetic means of operators in Fréchet spaces. J. Math. Anal. Appl. 401, 160–173 (2013)Albanese, A.A., Bonet, J., Ricker, W.J.: Uniform mean ergodicity of C 0 -semigroups in a class of in Fréchet spaces. Funct. Approx. Comment. Math. 50, 307–349 (2014)Albanese, A.A., Bonet, J., Ricker, W.J.: On the continuous Cesà ro operator in certain function spaces. Positivity 19, 659–679 (2015)Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesà ro operator in the Fréchet spaces ℓ p + and L p - . Glasgow Math. J. (accepted)Arendt, W.: Gaussian estimates and interpolation of the spectrum in L p . Diff. Int. Equ. 7, 1153–1168 (1994)Bayart, F., Matheron, E.: Dynamics of linear operators. Cambridge Tracts in Mathematics, vol. 179. Cambridge University Press, Cambridge (2009)Boyd, D.W.: The spectrum of the Cesà ro operator. Acta Sci. Math. (Szeged) 29, 31–34 (1968)Grosse-Erdmann, K.G., Manguillot, A.P.: Linear chaos. Universitext, Springer Verlag, London (2011)Hille, E.: Remarks on ergodic theorems. Trans. Am. Math. Soc. 57, 246–269 (1945)Jarchow, H.: Locally convex spaces. Teubner, Stuttgart (1981)Komura, T.: Semigroups of operators in locally convex spaces. J. Funct. Anal. 2, 258–296 (1968)Lin, M.: On the uniform ergodic theorem. Proc. Am. Math. Soc. 43, 337–340 (1974)Malgrange, B.: Idéaux de fonctions différentiables et division des distributions. Distributions, Editions École Polytechnique, Palaiseau, pp. 1–21 (2003)Meise, R., Vogt, D.: Introduction to functional analysis. Oxford Graduate Texts in Mathematics, vol. 2. The Clarendon Press. Oxford University Press, New York (1997)Seeley, R.T.: Extension of C ∞ functions defined in a half space. Proc. Am. Math. Soc. 15, 625–626 (1964)Siskakis, A.G.: Composition semigroups and the Cesà ro operator. J. London Math. Soc. (2) 36, 153–164 (1987)Yosida, K.: Functional analysis. Springer, New York, Berlin, Heidelberg (1980)Valdivia, M.: Topics in locally convex spaces. North-Holland Math. Stud. 67, North-Holland, Amsterdam (1982
Lunar laser ranging in infrfared at hte Grasse laser station
For many years, lunar laser ranging (LLR) observations using a green
wavelength have suffered an inhomogeneity problem both temporally and
spatially. This paper reports on the implementation of a new infrared detection
at the Grasse LLR station and describes how infrared telemetry improves this
situation. Our first results show that infrared detection permits us to densify
the observations and allows measurements during the new and the full Moon
periods. The link budget improvement leads to homogeneous telemetric
measurements on each lunar retro-reflector. Finally, a surprising result is
obtained on the Lunokhod 2 array which attains the same efficiency as Lunokhod
1 with an infrared laser link, although those two targets exhibit a
differential efficiency of six with a green laser link
String breaking
We numerically investigate the transition of the static quark-antiquark
string into a static-light meson-antimeson system. Improving noise reduction
techniques, we are able to resolve the signature of string breaking dynamics
for Nf=2 lattice QCD at zero temperature. We discuss the lattice techniques
used and present results on energy levels and mixing angle of the static
two-state system. We visualize the action density distribution in the region of
string breaking as a function of the static colour source-antisource
separation. The results can be related to properties of quarkonium systems.Comment: 8 pages, Talk given at the Workshop on Computational Hadron Physics,
Nicosia, Cyprus, 14--17 September 200
Scalar-gauge dynamics in (2+1) dimensions at small and large scalar couplings
We present the results of a detailed calculation of the excitation spectrum
of states with quantum numbers J^{PC}=0++, 1-- and 2++ in the three-dimensional
SU(2) Higgs model at two values of the scalar self-coupling and for fixed gauge
coupling. In the context of studies of the electroweak phase transition at
finite temperature these couplings correpond to tree-level, zero temperature
Higgs masses of 35 GeV and 120 GeV, respectively. We also study the properties
of Polyakov loop operators, which serve to test the confining properties of the
model in the symmetric phase. At both values of the scalar coupling we obtain
masses of bound states consisting entirely of gauge degrees of freedom
("W-balls"), which are very close to those obtained in the pure gauge theory.
We conclude that the previously observed, approximate decoupling of the scalar
and gauge sectors of the theory persists at large scalar couplings. We study
the crossover region at large scalar coupling and present a scenario how the
confining properties of the model in the symmetric phase are lost inside the
crossover by means of flux tube decay. We conclude that the underlying dynamics
responsible for the observed dense spectrum of states in the Higgs region at
large couplings must be different from that in the symmetric phase.Comment: 36 pages, LaTeX, 13 postscript files, to be included with epsf;
improved presentation, updated references, conclusions unchanged; version to
appear in Nucl. Phys.
On the flux phase conjecture at half-filling: an improved proof
We present a simplification of Lieb's proof of the flux phase conjecture for
interacting fermion systems -- such as the Hubbard model --, at half filling on
a general class of graphs. The main ingredient is a procedure which transforms
a class of fermionic Hamiltonians into reflection positive form. The method can
also be applied to other problems, which we briefly illustrate with two
examples concerning the model and an extended Falicov-Kimball model.Comment: 23 pages, Latex, uses epsf.sty to include 3 eps figures, to appear in
J. Stat. Phys., Dec. 199
The scalar and tensor glueballs in the valence approximation
We evaluate the infinite volume, continuum limit of and
glueball masses in the valence approximation. We find ~MeV and ~MeV, consistent with the interpretation
of as the lightest scalar glueball.Comment: (talk presented by A. Vaccarino at Lattice 93) 3 pages of PostScript
in uufiles compressed form. IBM-HET-94-
Another determination of the quark condensate from an overlap action
I use the technique of Hernandez, et al (hep-lat/0106011) to convert a recent
calculation of the lattice-regulated quark condensate from an overlap action to
a continuum-regulated number. I find Sigma(MSbar)(mu = 2 GeV) = (282(6)
MeV)-cubed times (a-inverse/1766 MeV)-cubed from a calculation with the Wilson
gauge action at beta=5.9.Comment: 3 pages, Revtex, 1 postscript figure. References added. COLO-HEP-47
Bounds on the Wilson Dirac Operator
New exact upper and lower bounds are derived on the spectrum of the square of
the hermitian Wilson Dirac operator. It is hoped that the derivations and the
results will be of help in the search for ways to reduce the cost of
simulations using the overlap Dirac operator. The bounds also apply to the
Wilson Dirac operator in odd dimensions and are therefore relevant to domain
wall fermions as well.Comment: 16 pages, TeX, 3 eps figures, small corrections and improvement
Operators on the Fréchet sequence space ces(p+),
[EN] The Fréchet sequence spaces ces(p+) are very different to the Fréchet sequence spaces ¿p+,1¿pp}\ell ^q ℓ p + = ∩ q > p ℓ q . Math. Nachr. 147, 7–12 (1990)Pérez Carreras, P., Bonet, J.: Barrelled Locally Convex Spaces. North Holland, Amsterdam (1987)Pitt, H.R.: A note on bilinear forms. J. Lond. Math. Soc. 11, 171–174 (1936)Ricker, W.J.: A spectral mapping theorem for scalar-type spectral operators in locally convex spaces. Integral Equ. Oper. Theory 8, 276–288 (1985)Robertson, A.P., Robertson, W.: Topological Vector Spaces. Cambridge University Press, Cambridge (1973)Waelbroeck, L.: Topological vector spaces and algebras. Lecture Notes in Mathematics, vol. 230. Springer, Berlin (1971
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