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Unconditional Schauder frames of translates in Lp(ℝd)
(Hebrew Univ Magnes Press, 2020-07)
We show that, for 1 < p ≤ 2, the space Lp(ℝd) does not admit unconditional Schauder frames {fi, f′i}i∈ℕ where {fi} is a sequence of translates of finitely many functions and {f′i} is seminormalized. In fact, the only ...
The reconstruction formula for Banach frames and duality
(Elsevier, 2011-02)
We study conditions on a Banach frame that ensures the validity of a reconstruction formula. In particular, we show that any Banach frames for (a subspace of) Lp or Lp,q (1≤p<∞) with respect to a solid sequence space always ...
EQUIVARIANT PATH FIELDS ON TOPOLOGICAL MANIFOLDS
(JULIUSZ SCHAUDER CTR NONLINEAR STUDIES, 2009)
A classical theorem of H. Hopf asserts that a closed connected smooth manifold admits a nowhere vanishing vector field if and only if its Euler characteristic is zero. R. Brown generalized Hopf`s result to topological ...
NATURAL TOPOLOGIES ON COLOMBEAU ALGEBRAS
(JULIUSZ SCHAUDER CTR NONLINEAR STUDIES, 2009)
We define intrinsic, natural and metrizable topologies T(Omega), T, T(s,Omega) and T(s) in G(Omega), (K) over bar, G(s)(Omega) and (K) over bar (s) respectively. The topology T(Omega) induces T, T(s,Omega) and T(s). The ...
NIELSEN COINCIDENCE THEORY OF FIBRE-PRESERVING MAPS AND DOLD`S FIXED POINT INDEX
(JULIUSZ SCHAUDER CTR NONLINEAR STUDIES, 2009)
Let M -> B, N -> B be fibrations and f(1), f(2): M -> N be a pair of fibre-preserving maps. Using normal bordism techniques we define an invariant which is an obstruction to deforming the pair f(1), f(2) over B to a ...
ABELIANIZED OBSTRUCTION FOR FIXED POINTS OF FIBER-PRESERVING MAPS OF SURFACE BUNDLES
(JULIUSZ SCHAUDER CTR NONLINEAR STUDIES, 2009)
Let f: M -> M be a fiber-preserving map where S -> M -> B is a bundle and S is a closed surface. We study the abelianized obstruction, which is a cohomology class in dimension 2, to deform f to a fixed point free map by a ...
GENERICITY OF NONDEGENERATE GEODESICS WITH GENERAL BOUNDARY CONDITIONS
(JULIUSZ SCHAUDER CTR NONLINEAR STUDIES, 2010)
Let M be a possibly noncompact manifold. We prove, generically in the C(k)-topology (2 <= k <= infinity), that semi-Riemannian metrics of a given index on M do not possess any degenerate geodesics satisfying suitable ...