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Semispectral Measures and Feller markov Kernels
Semispectral Measure Markov Kernel C-algebras Quantum Mechanics
2012/7/11
It is well known \cite{B1,P} that a real positive semispectral measure $F$ is commutative if and only if there exist a self-adjoint operator $A$ and a Markov kernel $\mu_{(\cdot)}(\cdot):\sigma(A)\tim...
Pointwise multipliers of Calderón-Lozanovskii spaces
Banach ideal spaces Banach function spaces Calderon-Lozanovskii spaces symmetric spaces Orlicz spaces sequence spaces
2012/6/30
Several results concerning multipliers of symmetric Banach function spaces are presented firstly. Then the results on multipliers of Calder\'on-Lozanovskii spaces are proved. We investigate assumption...
Linear independence of time-frequency translates of functions with faster than exponential decay
Gabor system exponential decay HRT conjecture linear independence timefrequency translates analytic zero divisor conjecture
2012/6/29
We establish the linear independence of time-frequency translates for functions $f$ having one sided decay $\lim_{x\to \infty} |f(x)| e^{cx \log x} = 0$ for all $c>0$. We also prove such results for f...
Average Number of Lattice Points in a Disk
lattice points Weyl asymptotics Bessel function
2012/6/29
The difference between the number of lattice points in a disk of radius $\sqrt{t}/2\pi$ and the area of the disk $t/4\pi$ is equal to the error in the Weyl asymptotic estimate for the eigenvalue count...
A Note on Coulhon type inequalities
Sobolev inequalities modulus of continuity symmetrization isoperimetric inequalities interpolation
2012/6/29
T. Coulhon introduced an interesting parametrization of Sobolev inequalities. We characterize Coulhon type inequalities in terms of rearrangement inequalities.
Exact spectrum of the Laplacian on a domain in the Sierpinski gasket
Sierpinski gasket Laplacian eigenvalues spectral decimation analysis on fractals
2012/6/27
For a certain domain $\Omega$ in the Sierpinski gasket $\mathcal{SG}$ whose boundary is a line segment, a complete description of the eigenvalues of the Laplacian under the Dirichlet and Neumann bound...
Estimates for approximation numbers of some classes of composition operators on the Hardy space
approximation numbers Blaschke product composition operator cusp map Hardy space modulus of continuity Schatten classes
2012/6/21
We give estimates for the approximation numbers of composition operators on $H^2$, in terms of some modulus of continuity. For symbols whose image is contained in a polygon, we get that these approxim...
Infinitesimal Carleson property for weighted measures induced by analytic self-maps of the unit disk
Calderón-Zygmund decomposition Carleson measure weighted Bergman space
2012/6/21
We prove that, for every $\alpha > -1$, the pull-back measure $\phi ({\cal A}_\alpha)$ of the measure $d{\cal A}_\alpha (z) = (\alpha + 1) (1 - |z|^2)^\alpha \, d{\cal A} (z)$, where ${\cal A}$ is the...
On the asymptotics of a Toeplitz determinant with singularities
the asymptotics of a Toeplitz determinant singularities Functional Analysis
2012/6/25
We provide an alternative proof of the classical single-term asymptotics for Toeplitz determinants whose symbols possess Fisher-Hartwig singularities. We also relax the smoothness conditions on the re...
A hereditarily indecomposable Banach space with rich spreading model structure
Spreading models Strictly singular operators Reflexive spaces Hereditarily indecomposable spaces
2012/6/25
We present a reflexive Banach space $\mathfrak{X}_{_{^\text{usm}}}$ which is Hereditarily Indecomposable and satisfies the following properties. In every subspace $Y$ of $\mathfrak{X}_{_{^\text{usm}}}...
New examples of K-monotone weighted Banach couples
K-monotone couples w-decomposable Banach lattices symmetric spaces ultrasymmetric spaces weighted symmetric spaces Lorentz spaces
2012/6/25
Some new examples of K-monotone couples of the type (X, X(w)), where X is a symmetric space on [0, 1] and w is a weight on [0, 1], are presented. Based on the property of the w-decomposability of a sy...
We give a brief overview of the area of Banach algebras, intended for a general mathematical audience.
Formulating Szemeredi's Theorem in Terms of Ultrafilters
Formulating Szemeredi's Theorem Terms of Ultrafilters Functional Analysis
2012/6/21
Van der Waerden's theorem asserts that if you color the natural numbers with, say, five different colors, then you can always find arbitrarily long sequences of numbers that have the same color and th...
Uniform families of ergodic operator nets
amenable semigroups mean ergodic theorem topological Wiener-Wintner theorems
2012/6/21
We study mean ergodicity in amenable operator semigroups and establish the connection to the convergence of strong and weak ergodic nets. We then use these results in order to show the convergence of ...
Heat equation for weighted Banach space valued function spaces
Laplace operator holomorphic semigroups weighted Banach space valued function spaces Functional Analysis
2012/6/21
We study the homogeneous equation (*) $ u' = \Delta u$, $t > 0$, $u(0)=f\in wX$, where $wX$ is a weighted Banach space, $w(x)= (1+||x||)^k$, $x\in \r^n$ with $k\ge 0$, $ \Delta$ is the Laplacian, $Y$ ...