Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Shannon Bishop
by alspach＠fourier.math.okstate.edu 08 Sep '09

08 Sep '09

This is an announcement for the paper "Mixed modulation spaces and their application to pseudodifferential operators" by Shannon Bishop. Abstract: This paper uses frame techniques to characterize the Schatten class properties of integral operators. The main result shows that if the coefficients of certain frame expansions of the kernel of an integral operator are in $ \ell^{2,p} $, then the operator is Schatten p-class. As a corollary, we conclude that if the kernel or Kohn-Nirenberg symbol of a pseudodifferential operator lies in a particular mixed modulation space, then the operator is Schatten p-class. Our corollary improves existing Schatten class results for pseudodifferential operators and the corollary is sharp in the sense that larger mixed modulation spaces yield operators that are not Schatten class. Archive classification: math.FA math.CA Mathematics Subject Classification: 35S05 (Primary) 42C15, 47B10 (Secondary) Remarks: To be published in Journal of Mathematical Analysis and Applications The source file(s), genmodshortD3.tex: 53295 bytes, is(are) stored in gzipped form as 0908.3420.gz with size 13kb. The corresponding postcript file has gzipped size 108kb. Submitted from: sbishop(a)math.gatech.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0908.3420 or http://arXiv.org/abs/0908.3420 or by email in unzipped form by transmitting an empty message with subject line uget 0908.3420 or in gzipped form by using subject line get 0908.3420 to: math(a)arXiv.org.

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Abstract of a paper by Joaquim Martin and Mario Milman
by alspach＠fourier.math.okstate.edu 08 Sep '09

08 Sep '09

This is an announcement for the paper "Pointwise symmetrization inequalities for Sobolev functions and applications" by Joaquim Martin and Mario Milman. Abstract: We develop a technique to obtain new symmetrization inequalities that provide a unified framework to study Sobolev inequalities, concentration inequalities and sharp integrability of solutions of elliptic equations Archive classification: math.FA math.AP The source file(s), martin-milman-symm.tex: 205567 bytes, is(are) stored in gzipped form as 0908.1751.gz with size 53kb. The corresponding postcript file has gzipped size 289kb. Submitted from: mario.milman(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0908.1751 or http://arXiv.org/abs/0908.1751 or by email in unzipped form by transmitting an empty message with subject line uget 0908.1751 or in gzipped form by using subject line get 0908.1751 to: math(a)arXiv.org.

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Abstract of a paper by Kevin Beanland
by alspach＠fourier.math.okstate.edu 08 Sep '09

08 Sep '09

This is an announcement for the paper "An ordinal index on the space of strictly singular operators" by Kevin Beanland. Abstract: Using the notion of $S_\xi$-strictly singular operator introduced by Androulakis, Dodos, Sirotkin and Troitsky, we define an ordinal index on the subspace of strictly singular operators between two separable Banach spaces. In our main result, we provide a sufficient condition implying that this index is bounded by $\omega_1$. In particular, we apply this result to study operators on totally incomparable spaces, hereditarily indecomposable spaces and spaces with few operators. Archive classification: math.FA Mathematics Subject Classification: 46B28; 03E15 Remarks: 8 pages The source file(s), , is(are) stored in gzipped form as with size . The corresponding postcript file has gzipped size . Submitted from: kbeanland(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0908.1113 or http://arXiv.org/abs/0908.1113 or by email in unzipped form by transmitting an empty message with subject line uget 0908.1113 or in gzipped form by using subject line get 0908.1113 to: math(a)arXiv.org.

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Abstract of a paper by Maxim V. Balashov and Dusan Repovs
by alspach＠fourier.math.okstate.edu 08 Sep '09

08 Sep '09

This is an announcement for the paper "Uniform convexity and the splitting problem for selections" by Maxim V. Balashov and Dusan Repovs. Abstract: We continue to investigate cases when the Repov\v{s}-Semenov splitting problem for selections has an affirmative solution for continuous set-valued mappings. We consider the situation in infinite-dimensional uniformly convex Banach spaces. We use the notion of Polyak of uniform convexity and modulus of uniform convexity for arbitrary convex sets (not necessary balls). We study general geometric properties of uniformly convex sets. We also obtain an affirmative solution of the splitting problem for selections of certain set-valued mappings with uniformly convex images. Archive classification: math.GN math.FA Mathematics Subject Classification: 54C60; 54C65; 52A07; 46A55; 52A01 Citation: J. Math. Anal. Appl. 360:1 (2009), 307-316 The source file(s), balashov+repovs2-final.tex: 49005 bytes, is(are) stored in gzipped form as 0908.1216.gz with size 15kb. The corresponding postcript file has gzipped size 91kb. Submitted from: dusan.repovs(a)guest.arnes.si The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0908.1216 or http://arXiv.org/abs/0908.1216 or by email in unzipped form by transmitting an empty message with subject line uget 0908.1216 or in gzipped form by using subject line get 0908.1216 to: math(a)arXiv.org.

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New email address for M Ledoux
by Dale Alspach 03 Sep '09

03 Sep '09

Dear colleagues, please note my new email address ledoux(a)math.univ-toulouse.fr Sincerely yours. M. Ledoux

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Abstract of a paper by Kevin Beanland
by Dale Alspach 17 Aug '09

17 Aug '09

This is an announcement for the paper "Operators on asymptotic $\ell_p$ spaces which are not compact perturbations of a multiple of the identity" by Kevin Beanland. Abstract: We give sufficient conditions on an asymptotic $\ell_p$ (for $1 < p < \infty$) Banach space which ensure the space admits an operator which is not a compact perturbation of a multiple of the identity. These conditions imply the existence of strictly singular non-compact operators on the HI spaces constructed by G. Androulakis and the author and by I. Deliyanni and A. Manoussakis. Additionally we show that under these same conditions on the space $X$, $\ell_\infty$ embeds isomorphically into the space of bounded linear operators on $X$. Archive classification: math.FA The source file(s), SSnonCPT.tex: 51728 bytes, is(are) stored in gzipped form as 0908.1107.gz with size 16kb. The corresponding postcript file has gzipped size 120kb. Submitted from: kbeanland(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0908.1107 or http://arXiv.org/abs/0908.1107 or by email in unzipped form by transmitting an empty message with subject line uget 0908.1107 or in gzipped form by using subject line get 0908.1107 to: math(a)arXiv.org.

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Abstract of a paper by Elena Ournycheva and Boris Rubin
by alspach＠fourier.math.okstate.edu 17 Aug '09

17 Aug '09

This is an announcement for the paper "On Y. Nievergelt's inversion formula for the Radon transform" by Elena Ournycheva and Boris Rubin. Abstract: We generalize Y. Nievergelt's inversion method for the Radon transform on lines in the 2-plane to the $k$-plane Radon transform of continuous and $L^p$ functions on $R^n$ for all $1\leq k<n$. Archive classification: math.FA Mathematics Subject Classification: Primary 42C40; Secondary 44A12 Remarks: 9 pages The source file(s), niev-amsproc4.tex: 29069 bytes, is(are) stored in gzipped form as 0908.0492.gz with size 10kb. The corresponding postcript file has gzipped size 78kb. Submitted from: elo10(a)pitt.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0908.0492 or http://arXiv.org/abs/0908.0492 or by email in unzipped form by transmitting an empty message with subject line uget 0908.0492 or in gzipped form by using subject line get 0908.0492 to: math(a)arXiv.org.

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Abstract of a paper by Stephen Simons
by alspach＠fourier.math.okstate.edu 17 Aug '09

17 Aug '09

This is an announcement for the paper "Banach SSD spaces and classes of monotone sets" by Stephen Simons. Abstract: In this paper, we unify the theory of SSD spaces and the theory of strongly representable sets, and we apply our results to the theory of the various classes of maximally monotone sets. We obtain some new results about these, as well as some new proofs of old ones. Archive classification: math.FA Mathematics Subject Classification: 47H05, 47N10, 46N10 The source file(s), SSDMONarxiv.tex: 116002 bytes, is(are) stored in gzipped form as 0908.0383.gz with size 29kb. The corresponding postcript file has gzipped size 133kb. Submitted from: simons(a)math.ucsb.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0908.0383 or http://arXiv.org/abs/0908.0383 or by email in unzipped form by transmitting an empty message with subject line uget 0908.0383 or in gzipped form by using subject line get 0908.0383 to: math(a)arXiv.org.

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Abstract of a paper by Benoit Kloeckner
by alspach＠fourier.math.okstate.edu 17 Aug '09

17 Aug '09

This is an announcement for the paper "Sharp quantitative isoperimetric inequalities in the $L^1$ Minkowski plane" by Benoit Kloeckner. Abstract: We prove that a plane domain which is almost isoperimetric (with respect to the $L^1$ metric) is close to a square whose sides are parallel to the coordinates axis. Closeness is measured either by $L^\infty$ Haussdorf distance or Fraenkel asymmetry. In the first case, we determine the extremal domains. Archive classification: math.FA math.DG Mathematics Subject Classification: MSC 51M16, 51M25, 49Q20 Remarks: 9 pages The source file(s), central_square.pstex: 6034 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0907.4945 or http://arXiv.org/abs/0907.4945 or by email in unzipped form by transmitting an empty message with subject line uget 0907.4945 or in gzipped form by using subject line get 0907.4945 to: math(a)arXiv.org.

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Abstract of a paper by Stephan Ramon Garcia and Warren R. Wogen
by alspach＠fourier.math.okstate.edu 17 Aug '09

17 Aug '09

This is an announcement for the paper "Complex symmetric partial isometries" by Stephan Ramon Garcia and Warren R. Wogen. Abstract: An operator $T \in B(\h)$ is complex symmetric if there exists a conjugate-linear, isometric involution $C:\h\to\h$ so that $T = CT^*C$. We provide a concrete description of all complex symmetric partial isometries. In particular, we prove that any partial isometry on a Hilbert space of dimension $\leq 4$ is complex symmetric. Archive classification: math.FA math.OA Mathematics Subject Classification: 47B99 Citation: J. Funct. Analysis 257 (2009), 1251-1260 Remarks: 9 pages The source file(s), CSPI.tex: 33368 bytes, is(are) stored in gzipped form as 0907.4486.gz with size 10kb. The corresponding postcript file has gzipped size 68kb. Submitted from: Stephan.Garcia(a)pomona.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0907.4486 or http://arXiv.org/abs/0907.4486 or by email in unzipped form by transmitting an empty message with subject line uget 0907.4486 or in gzipped form by using subject line get 0907.4486 to: math(a)arXiv.org.

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