The Experts below are selected from a list of 162 Experts worldwide ranked by ideXlab platform
Andrea Marchese - One of the best experts on this subject based on the ideXlab platform.
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residually many bv homeomorphisms map a Null Set in a Set of full measure
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2019Co-Authors: Andrea MarcheseAbstract:Let Q = (0,1) 2 be the unit square in R 2 . We prove that in a suitable complete metric space of BV homeomorphisms f : Q → Q with f|@Q = Id, the generical homeomorphism (in the sense of Baire categories) maps a Null Set in a Set of full measure and vice versa. Moreover we observe that, for 1 ≤ p < 2, in the most reasonable complete metric space for such problem, the family of W 1,p homemomorphisms satisfying the above property is of first category, instead.
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residually many bv homeomorphisms map a Null Set in a Set of full measure
arXiv: Functional Analysis, 2015Co-Authors: Andrea MarcheseAbstract:Let $Q=(0,1)^2$ be the unit square in $\mathbb{R}^2$. We prove that in a suitable complete metric space of $BV$ homeomorphisms $f:Q\rightarrow Q$ with $f_{|\partial Q}=Id$, the generical homeomorphism (in the sense of Baire categories) maps a Null Set in a Set of full measure and vice versa. Moreover we observe that, for $1\leq p<2$, in the most reasonable complete metric space for such problem, the family of $W^{1,p}$ homemomorphisms satisfying the above property is of first category, instead.
Danyu Yang - One of the best experts on this subject based on the ideXlab platform.
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the partial sum process of orthogonal expansions as geometric rough process with fourier series as an example an improvement of menshov rademacher theorem
Journal of Functional Analysis, 2013Co-Authors: Terry Lyons, Danyu YangAbstract:Abstract The partial sum process of orthogonal expansion ∑ n ⩾ 0 c n u n is a geometric 2-rough process, for any orthonormal system { u n } n ⩾ 0 in L 2 and any sequence of numbers { c n } satisfying ∑ n ⩾ 0 ( log 2 ( n + 1 ) ) 2 | c n | 2 ∞ . Since being a geometric 2-rough process implies the existence of a limit function up to a Null Set, our theorem could be treated as an improvement of Menshov–Rademacher theorem. For Fourier series, the condition can be strengthened to ∑ n ⩾ 0 log 2 ( n + 1 ) | c n | 2 ∞ , which is equivalent to ∫ − π π ∫ − π π | f ( u ) − f ( v ) | 2 | sin u − v 2 | d u d v ∞ (with f the limit function).
Terry Lyons - One of the best experts on this subject based on the ideXlab platform.
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the partial sum process of orthogonal expansions as geometric rough process with fourier series as an example an improvement of menshov rademacher theorem
Journal of Functional Analysis, 2013Co-Authors: Terry Lyons, Danyu YangAbstract:Abstract The partial sum process of orthogonal expansion ∑ n ⩾ 0 c n u n is a geometric 2-rough process, for any orthonormal system { u n } n ⩾ 0 in L 2 and any sequence of numbers { c n } satisfying ∑ n ⩾ 0 ( log 2 ( n + 1 ) ) 2 | c n | 2 ∞ . Since being a geometric 2-rough process implies the existence of a limit function up to a Null Set, our theorem could be treated as an improvement of Menshov–Rademacher theorem. For Fourier series, the condition can be strengthened to ∑ n ⩾ 0 log 2 ( n + 1 ) | c n | 2 ∞ , which is equivalent to ∫ − π π ∫ − π π | f ( u ) − f ( v ) | 2 | sin u − v 2 | d u d v ∞ (with f the limit function).
Pandelis Dodos - One of the best experts on this subject based on the ideXlab platform.
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dichotomies of the Set of test measures of a haar Null Set
arXiv: Functional Analysis, 2010Co-Authors: Pandelis DodosAbstract:We prove that if $X$ is a Polish space and $F$ is a face of $P(X)$ with the Baire property, then $F$ is either a meager or a co-meager subSet of $P(X)$. As a consequence we show that for every abelian Polish group $X$ and every analytic Haar-Null Set $A\subSeteq X$, the Set of test measures $T(A)$ of $A$ is either meager or co-meager. We characterize the non-locally-compact groups as the ones for which there exists a closed Haar-Null Set $F\subSeteq X$ with $T(F)$ is meager. Moreover, we answer negatively a question of J. Mycielski by showing that for every non-locally-compact abelian Polish group and every $\sigma$-compact subgroup $G$ of $X$ there exists a $G$-invariant $F_\sigma$ subSet of $X$ which is neither prevalent nor Haar-Null.
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dichotomies of the Set of test measures of a haar Null Set
Israel Journal of Mathematics, 2004Co-Authors: Pandelis DodosAbstract:We prove that ifX is a Polish space andF a face ofP(X) with the Baire property, thenF is either a meager or a co-meager subSet ofP(X). As a consequence we show that for every abelian Polish groupX and every analytic Haar-Null Set Λ⊆X, the Set of test measuresT(Λ) of Λ is either meager or co-meager. We characterize the non-locally-compact groups as the ones for which there exists a closed Haar-Null SetF⊆X withT(F) meager, Moreover, we answer negatively a question of J. Mycielski by showing that for every non-locally-compact abelian Polish group and every σ-compact subgroupG ofX there exists aG-invariantF σ subSet ofX which is neither prevalent nor Haar-Null.
Yu I Popov - One of the best experts on this subject based on the ideXlab platform.
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two physical applications of the laplace operator perturbed on a Null Set
Theoretical and Mathematical Physics, 1999Co-Authors: D A Zubok, Yu I PopovAbstract:Two physical applications of the Laplace operator perturbed on a Set of zero measure are suggested. The approach is based on the theory of self-adjoint extensions of symmetrical operators. The first applicatio is a solvable model of scattering of a plane wave by a perturbed thin cylinder. “Nonlocal” extensions are described. The model parameters can be chosen such that the model solution is an approximation of the corresponding “realistic” solution. The second application is the description of the time evolution of a one-dimensional quasi-Chaplygin medium, which can be reduced using a hodograph transform to the ill-posed problem of the Laplace operator perturbed on a Set of codimension two inR3. Stability and instability conditions are obtained.
