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Non-consistent approximations of self-adjoint eigenproblems: Application to the supercell method
Non-consistent approximations self-adjoint eigenproblems Functional Analysis
2012/5/24
In this article, we introduce a general theoretical framework to analyze non-consistent approximations of the discrete eigenmodes of a self-adjoint operator. We focus in particular on the discrete eig...
Restricted normal cones and the method of alternating projections
Constraint qualification convex set Friedrichs angle linear convergence method of alternating projections
2012/5/24
The method of alternating projections (MAP) is a common method for solving feasibility problems. While employed traditionally to subspaces or to convex sets, little was known about the behavior of the...
Dependence of Kolmogorov widths on the ambient space
Dependence of Kolmogorov widths ambient space Functional Analysis
2012/5/9
We study the dependence of the Kolmogorov widths of a compact set on the ambient Banach space.
Pointwise convergence of vector-valued Fourier series
Pointwise convergence vector-valued Fourier series Functional Analysis
2012/5/24
We prove a vector-valued version of Carleson's theorem: Let Y=[X,H]_t be a complex interpolation space between a UMD space X and a Hilbert space H. For p\in(1,\infty) and f\in L^p(T;Y), the partial su...
Oversampling of wavelet frames for real dilations
wavelets affine frames real dilations Second Oversampling Theorem shift invariant subspaces
2012/4/16
We generalize the Second Oversampling Theorem for wavelet frames and dual wavelet frames from the setting of integer dilations to real dilations. We also study the relationship between dilation matrix...
A characterization of amenability of group actions on $C^\ast$-algebras
characterization amenability group actions $C^\ast$-algebras
2012/4/16
We show that coincidence of the full and reduced crossed product $C^\ast$-algebras of a group action on a unital commutative $C^\ast$-algebra implies amenability of the action whenever the group is ex...
Real analytic expansion of spectral projection and extension of Hecke-Bochner identity
Coxeter group Hecke-Bochner identity Heisenberg group Laguerre polynomials spherical harmonics twisted convolution
2012/4/16
In this article, we review the Weyl correspondence of bigraded spherical harmonics and use it to extend the Hecke-Bochner identities for the spectral projections $f\times\varphi_k^{n-1}$ for function ...
Oriented Associativity Equations and Symmetry Consistent Conjugate Curvilinear Coordinate Nets
Oriented Associativity Equations Symmetry Consistent Conjugate Curvilinear Coordinate Nets Exactly Solvable and Integrable Systems
2012/4/26
This paper is devoted to description of the relationship among oriented associativity equations, symmetry consistent conjugate curvilinear coordinate nets, and the widest associated class of semi- Ham...
Reducing scattering problems under cone potentials to normal form by global canonical transformations
scattering problems cone normal form global canonical transformations Exactly Solvable and Integrable Systems
2012/4/26
We introduce a class of Hamiltonian scattering systems which can be reduced to the "normal form" $\dot P=0$, $\dot Q=P$, by means of a global canonical transformation $ (P,Q)=A(p,q), p,q\in R^n$, defi...
Necessary conditions for variational regularization schemes
Variational regularization Tikhonov regularization necessary conditions general discrepancy term Bregman distances
2012/4/18
We study variational regularization methods in a general framework, more precisely those methods that use a discrepancy and a regularization functional. While several sets of sufficient conditions are...
Some Remarks On Essentially Normal Submodules
Arveson conjecture essentially normal submodules Functional Analysis
2012/4/18
Given a *-homomorphism $\sigma: C(M)\to \mathscr{L}(\mathcal{H})$ on a Hilbert space $\mathcal{H}$ for a compact metric space $M$, a projection $P$ onto a subspace $\mathcal{P}$ in $\mathcal{H}$ is sa...
Anisotropic Function Spaces on Singular Manifolds
Anisotropic weighted Sobolev spaces Bessel potential spaces Besov spaces Holder spaces noncomplete Riemannian manifolds with boundary
2012/4/18
A rather complete investigation of anisotropic Bessel potential, Besov, and H\"older spaces on cylinders over (possibly) noncompact Riemannian manifolds with boundary is carried out. The geometry of t...
On Self-Adjointness Of 1-D Schrodinger Operators With $δ$-Interactions
Schrodinger operator local point interaction self-adjoint operator deficiency indices Jacobi matrices
2012/4/23
In the present work we consider in $L^2(\mathbb{R}_+)$ the Schr\"odinger operator $\mathrm{H_{X,\alpha}}=-\mathrm{\frac{d^2}{dx^2}}+\sum_{n=1}^{\infty}\alpha_n\delta(x-x_n)$. We investigate and comple...
Creator-annihilator domains and the number operator
Creator-annihilator domains the number operator Functional Analysis
2012/4/23
We show that for the bosonic Fock representation in infinite dimensions, the maximal common domain of all creators and annihilators properly contains the domain of the square-root of the number operat...
Free evolution on algebras with two states II
Free evolution algebras two states II Operator Algebras
2012/4/17
Denote by $J$ the operator of coefficient stripping. We show that for any free convolution semigroup of measures $\nu_t$ with finite variance, applying a single stripping produces semicircular evoluti...