Results 41 to 50 of about 8,384 (123)
Binary Operations in Metric Spaces Satisfying Side Inequalities
Mathematics, 2021 The theory of metric spaces is a convenient and very powerful way of examining the behavior of numerous mathematical models. In a previous paper, a new operation between functions on a compact real interval called fractal convolution has been introduced.
María A. Navascués +2 more
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Riesz bases of reproducing kernels in Fock type spaces
, 2009 In a scale of Fock spaces $\mathcal F_\varphi$ with radial weights $\varphi$ we study the existence of Riesz bases of (normalized) reproducing kernels. We prove that these spaces possess such bases if and only if $\varphi(x)$ grows at most like $(\log x)^
Borichev, A., Lyubarskii, Yu.
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Hamiltonians with Riesz Bases of Generalised Eigenvectors and Riccati Equations [PDF]
, 2010 An algebraic Riccati equation for linear operators is studied, which arises in systems theory. For the case that all involved operators are unbounded, the existence of infinitely many selfadjoint solutions is shown. To this end, invariant graph subspaces
Wyss, Christian
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Characterizing Riesz Bases via Biorthogonal Riesz-Fischer sequences
, 2022 In this note we prove that if two Riesz-Fischer sequences in a separable Hilbert space $H$ are biorthogonal and one of them is complete in $H$, then both sequences are Riesz bases for $H$. This complements a recent result by D. T. Stoeva where the same conclusion holds if one replaces the phrase ``Riesz-Fischer sequences'' by ``Bessel sequences''.
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Construction of pseudo-bosons systems [PDF]
, 2010 In a recent paper we have considered an explicit model of a PT-symmetric system based on a modification of the canonical commutation relation. We have introduced the so-called {\em pseudo-bosons}, and the role of Riesz bases in this context has been ...
F. Bagarello, Kolmogorov A., Young R.
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On Construction of Bounded Sets Not Admitting a General Type of Riesz Spectrum
AxiomsWe construct a bound set that does not admit a Riesz spectrum containing a nonempty periodic set for which the period is a rational multiple of a fixed constant.
Dae Gwan Lee
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, 2013 In this paper, we give some sufficient conditions under which perturbations preserve Hilbert frames and near-Riesz bases. Similar results are also extended to frame sequences, Riesz sequences and Schauder frames.
Chen, Dongyang, Li, Lei, Zheng, Bentuo
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Non-self-adjoint hamiltonians defined by Riesz bases [PDF]
Journal of Mathematical Physics, 2014 We discuss some features of non-self-adjoint Hamiltonians with real discrete simple spectrum under the assumption that the eigenvectors form a Riesz basis of Hilbert space. Among other things, we give conditions under which these Hamiltonians can be factorized in terms of generalized lowering and raising operators.
Bagarello, F., Inoue, A., Trapani, C.
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Linear combinations of frame generators in systems of translates [PDF]
, 2013 A finitely generated shift invariant space $V$ is a closed subspace of $L^2(\R^d)$ that is generated by the integer translates of a finite number of functions.
Cabrelli, Carlos +2 more
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Riesz bases, Meyer’s quasicrystals, and bounded remainder sets [PDF]
Transactions of the American Mathematical Society, 2018 We consider systems of exponentials with frequencies belonging to simple quasicrystals in $\mathbb{R}^d$. We ask if there exist domains $S$ in $\mathbb{R}^d$ which admit such a system as a Riesz basis for the space $L^2(S)$. We prove that the answer depends on an arithmetical condition on the quasicrystal.
Grepstad, Sigrid, Lev, Nir
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