Related papers: Refuting a Recent Proof of the Invariant Subspace …
The invariant subspace problem is solved correcting my earlier attempts [6]-[12].
We prove the Invariant Subspace Conjecture for separable Hilbert spaces.
The hyperinvariant subspace problem is solved in the setting of Hilbert and right Hamilton space, motivated by my earlier works in the invariant subspace problem.
This paper has been withdrawn by the author, since the author does not have enough time to answer every questions on this result.
In this article we study invariance properties of shift-invariant spaces in higher dimensions. We state and prove several necessary and sufficient conditions for a shift-invariant space to be invariant under a given closed subgroup of…
A shift-invariant space is a space of functions that is invariant under integer translations. Such spaces are often used as models for spaces of signals and images in mathematical and engineering applications. This paper characterizes those…
In this survey we give an overview of recent developments on the Quantitative Subspace Theorem. In particular, we discuss a new upper bound for the number of subspaces containing the "large" solutions, obtained jointly with Roberto…
We demonstrate the equivalence of two classes of $D$-invariant polynomial subspaces introduced in [8] and [9], i.e., these two classes of subspaces are different representations of the breadth-one $D$-invariant subspace. Moreover, we solve…
The present note refers to a result proposed in [Elhadj and Sprott, 2012], and shows that the Theorem therein is not correct. We explain that a proof of that Theorem cannot be given, as the statement is not correct, and we underline a…
This article has been withdrawn due to an error in a proof of the main result.
In this paper, we prove an inequality regarding the differential polynomial. This improves some recent results.
In this note we extend D. Singh and A. A. W. Mehanna's invariant subspace theorem for $RH^1$ (the real Banach space of analytic functions in $H^1$ with real Taylor coefficients) to the simply invariant subspaces of $RL^1$ (the real Banach…
This correspondence disproves the main results in the paper "Design of Asymmetric Shift Operators for Efficient Decentralized Subspace Projection" by S. Mollaebrahim and B. Beferull-Lozano. Counterexamples and counterproofs are provided…
In this note we show that given a conformally invariant theory in flat space-time, it is not always possible to couple it to gravity in a Weyl invariant way.
We introduce a notion of retraction between continuous maps of topological spaces and study the behavior of several numerical invariants under such retractions. These include (co)homological dimensions, the Lusternik-Schnirelmann category,…
We give an elementary proof of an efficient version of the Wagner's theorem on almost invariant subspaces and deduce some consequences in the context of Galois extensions.
In this paper, we give a new and short proof of a Theorem on k-hypertournament losing scores due to Zhou et al.[7].
We survey the problem of whether M_3 spaces are M_1 spaces.
We analyze the experiment recently realized by S. Afshar et al. [1] in order to refute the principle of complementarity. We discuss the general meaning of this principle and show that contrarily to the claim of the authors Bohr's…
This is a comment on recent paper by T.M. Stace and S.D. Barrett, PRL 92, 136802 (2004). We show that the main result of the paper, absence of the spectral peak for continuous weak measurement of coherent oscillations in a qubit, is…