Discrete convolution-rearrangement inequalities and the Faber-Krahn inequality on regular trees
Alexander R. Pruss
Source: Duke Math. J. Volume 91, Number 3
(1998), 463-514.
First Page:
Show
Hide
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077232256
Mathematical Reviews number (MathSciNet): MR1604163
Zentralblatt MATH identifier: 0943.05056
Digital Object Identifier: doi:10.1215/S0012-7094-98-09119-0
References
[1] II, Albert Baernstein, Integral means, univalent functions and circular symmetrization, Acta Math. 133 (1974), 139–169.
Mathematical Reviews (MathSciNet): MR54:5456
Zentralblatt MATH: 0315.30021
Digital Object Identifier: doi:10.1007/BF02392144
[2] II, Albert Baernstein, A unified approach to symmetrization, Partial differential equations of elliptic type (Cortona, 1992) ed. A. Alvino, et al., Sympos. Math., XXXV, Cambridge Univ. Press, Cambridge, 1994, pp. 47–91.
Mathematical Reviews (MathSciNet): MR96e:26019
Zentralblatt MATH: 0830.35005
[3] II, Albert Baernstein and B. A. Taylor, Spherical rearrangements, subharmonic functions, and $\sp*$-functions in $n$-space, Duke Math. J. 43 (1976), no. 2, 245–268.
Mathematical Reviews (MathSciNet): MR53:5906
Zentralblatt MATH: 0331.31002
Digital Object Identifier: doi:10.1215/S0012-7094-76-04322-2
Project Euclid: euclid.dmj/1077311636
[4] W. Beckner, Moser-Trudinger inequality in higher dimensions, Internat. Math. Res. Notices (1991), no. 7, 83–91.
Mathematical Reviews (MathSciNet): MR93a:58172
Zentralblatt MATH: 0756.58013
Digital Object Identifier: doi:10.1155/S1073792891000120
[5] W. Beckner, Sobolev inequalities, the Poisson semigroup, and analysis on the sphere $S\sp n$, Proc. Nat. Acad. Sci. U.S.A. 89 (1992), no. 11, 4816–4819.
Mathematical Reviews (MathSciNet): MR93d:26018
Zentralblatt MATH: 0766.46012
Digital Object Identifier: doi:10.1073/pnas.89.11.4816
JSTOR: links.jstor.org
[6] W. Beckner, Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality, Ann. of Math. (2) 138 (1993), no. 1, 213–242.
Mathematical Reviews (MathSciNet): MR94m:58232
Zentralblatt MATH: 0826.58042
Digital Object Identifier: doi:10.2307/2946638
JSTOR: links.jstor.org
[7] W. Beckner, Geometric inequalities in Fourier anaylsis, Essays on Fourier analysis in honor of Elias M. Stein (Princeton, NJ, 1991) eds. Charles Fefferman, Robert Fefferman, and Stephen Wainger, Princeton Math. Ser., vol. 42, Princeton Univ. Press, Princeton, NJ, 1995, pp. 36–68.
Mathematical Reviews (MathSciNet): MR95m:42004
Zentralblatt MATH: 0888.42006
[8] Arne Beurling, Études sur un problème de majoration, thesis, Almqvist & Wiksell, Uppsala, 1933.
[9] H. J. Brascamp, Elliott H. Lieb, and J. M. Luttinger, A general rearrangement inequality for multiple integrals, J. Functional Analysis 17 (1974), 227–237.
Mathematical Reviews (MathSciNet): MR49:10835
Zentralblatt MATH: 0286.26005
Digital Object Identifier: doi:10.1016/0022-1236(74)90013-5
[10] Jian Sheng Chen, Sharp bound of the $k$th eigenvalue of trees, Discrete Math. 128 (1994), no. 1-3, 61–72.
Mathematical Reviews (MathSciNet): MR95b:05141
Zentralblatt MATH: 0796.05067
Digital Object Identifier: doi:10.1016/0012-365X(94)90104-X
[11] C. Faber, Beweiss, dass unter allen homogenen Membrane von gleicher Fläche und gleicher Spannung die kreisförmige die tiefsten Grundton gibt, Sitzungsber. Bayer Akad. Wiss. Math. Phys., Munich. (1923), 169–172.
Zentralblatt MATH: 49.0342.03
[12] Joel Friedman, Some geometric aspects of graphs and their eigenfunctions, Duke Math. J. 69 (1993), no. 3, 487–525.
Mathematical Reviews (MathSciNet): MR94b:05134
Zentralblatt MATH: 0785.05066
Digital Object Identifier: doi:10.1215/S0012-7094-93-06921-9
Project Euclid: euclid.dmj/1077293725
[13] D. H. Griffel, Linear algebra and its applications. Vol. 2, Ellis Horwood Series: Mathematics and its Applications, Ellis Horwood Ltd., Chichester, 1989.
Mathematical Reviews (MathSciNet): MR90f:15001b
Zentralblatt MATH: 0668.15001
[14] Kersti Haliste, Estimates of harmonic measures, Ark. Mat. 6 (1965), 1–31 (1965).
Mathematical Reviews (MathSciNet): MR34:1547
Zentralblatt MATH: 0178.13801
Digital Object Identifier: doi:10.1007/BF02591325
[15] Frank Harary, Graph theory, Addison-Wesley Publishing Co., Reading, Mass.-Menlo Park, Calif.-London, 1969.
Mathematical Reviews (MathSciNet): MR41:1566
Zentralblatt MATH: 0182.57702
[16] G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge Univ. Press, Cambridge, 1964.
[17] E. Krahn, Über eine von Rayleigh formulierte Minimaleigenschafte des Kreises, Math. Ann. 94 (1925), 97–100.
Zentralblatt MATH: 51.0356.05
[18] Rolf Nevanlinna, Analytic functions, Translated from the second German edition by Phillip Emig. Die Grundlehren der mathematischen Wissenschaften, Band 162, Springer-Verlag, New York, 1970.
Mathematical Reviews (MathSciNet): MR43:5003
Zentralblatt MATH: 0199.12501
[19] Alexander R. Pruss, Discrete harmonic measure, Green's functions and symmetrization: A unified probabilistic approach, preprint, 1996.
[20] Alexander R. Pruss, Symmetrization, harmonic measures, Green's functions and difference equations, Ph.D. thesis, University of British Columbia, Vancouver, 1996.
[21] Alexander R. Pruss, Symmetrization inequalities for difference equations on graphs, to appear in Adv. Math.
Mathematical Reviews (MathSciNet): MR1675757
Zentralblatt MATH: 0922.39002
Digital Object Identifier: doi:10.1006/aama.1998.0636
[22] J. R. Quine, Symmetrization inequalities for discrete harmonic functions, preprint.
[23] J. W. S. (Lord) Rayleigh, The Theory of Sound, 2d ed., Macmillan, New York, 1877, reprint, Dover, New York, 1945.
Mathematical Reviews (MathSciNet): MR16009
[24] F. Riesz, Sur une inégalité intégrale, J. London Math. Soc. 5 (1930), 162–168.
Zentralblatt MATH: 56.0232.02
[N1] J. Leydold, A Faber-Krahn-type inequality for regular trees, Geom. Funct. Anal. 7 (1997), no. 2, 364–378.
Mathematical Reviews (MathSciNet): MR98c:05112
Zentralblatt MATH: 0892.05027
Digital Object Identifier: doi:10.1007/PL00001623
Duke Mathematical Journal