Some finite-dimensional backward-shift-invariant subspaces in the ball and a related interpolation problem

2002 ◽  
Vol 42 (1) ◽  
pp. 1-21 ◽  
Author(s):  
Daniel Alpay ◽  
H. Turgay Kaptanoğlu
Keyword(s):  
Interpolation Problem ◽  
Invariant Subspaces ◽  
Finite Dimensional ◽  
Backward Shift

scholarly journals Backward Shift and Nearly Invariant Subspaces of Fock-type Spaces

2021 ◽  
Author(s):  
Alexandru Aleman ◽  
Anton Baranov ◽  
Yurii Belov ◽  
Haakan Hedenmalm
Keyword(s):  
Exponential Type ◽  
Slow Growth ◽  
Invariant Subspaces ◽  
Dense Subspace ◽  
Finite Dimensional ◽  
Radial Case ◽  
Backward Shift ◽  
Type Spaces

Abstract We study the structure of the backward shift invariant and nearly invariant subspaces in weighted Fock-type spaces ${\mathcal{F}}_W^p$, whose weight is not necessarily radial. We show that in the spaces ${\mathcal{F}}_W^p$, which contain the polynomials as a dense subspace (in particular, in the radial case), all nontrivial backward shift invariant subspaces are of the form $\mathcal{P}_n$, that is, finite-dimensional subspaces consisting of polynomials of degree at most $n$. In general, the structure of the nearly invariant subspaces is more complicated. In the case of spaces of slow growth (up to zero exponential type), we establish an analogue of de Branges’ ordering theorem. We then construct examples that show that the result fails for general Fock-type spaces of larger growth.

scholarly journals Conditional Lie-Bäcklund Symmetries and Reductions of the Nonlinear Diffusion Equations with Source

2014 ◽  
Vol 2014 ◽  
pp. 1-17
Author(s):  
Junquan Song ◽  
Yujian Ye ◽  
Danda Zhang ◽  
Jun Zhang
Keyword(s):  
Invariant Subspace ◽  
Dynamic Systems ◽  
Nonlinear Diffusion ◽  
Invariant Subspaces ◽  
Higher Order ◽  
Diffusion Equations ◽  
Canonical Forms ◽  
Nonlinear Diffusion Equations ◽  
Symmetry Approach ◽  
Finite Dimensional

Conditional Lie-Bäcklund symmetry approach is used to study the invariant subspace of the nonlinear diffusion equations with sourceut=e−qx(epxP(u)uxm)x+Q(x,u),m≠1. We obtain a complete list of canonical forms for such equations admit multidimensional invariant subspaces determined by higher order conditional Lie-Bäcklund symmetries. The resulting equations are either solved exactly or reduced to some finite-dimensional dynamic systems.

CHAOS IN WAVE INTERACTIONS

2007 ◽  
Vol 17 (01) ◽  
pp. 85-98 ◽  
Author(s):  
Y. CHARLES LI
Keyword(s):  
Stokes Equation ◽  
Invariant Subspaces ◽  
Navier Stokes ◽  
Wave Interactions ◽  
Navier Stokes Equation ◽  
Finite Dimensional ◽  
Galerkin Truncation

Existence of chaos is proved in finite-dimensional invariant subspaces for both two- and three-wave interactions. For a simple Galerkin truncation of the 2D Navier–Stokes equation, existence of chaos is also proved.

scholarly journals Non-negative Integer Power of a Hyponormal m-isometry is Reflexive

2021 ◽  
pp. 1-5
Author(s):  
Pradeep Kothiyal ◽  
Rajesh Kumar Pal ◽  
Deependra Nigam
Keyword(s):  
Dimensional Space ◽  
Normal Operator ◽  
Invariant Subspaces ◽  
Negative Integer ◽  
Finite Dimensional Space ◽  
Integer Power ◽  
Finite Dimensional ◽  
Normal Operators ◽  
Reflexive Operator

Sarason did pioneer work on reflexive operator and reflexivity of normal operators, however, he did not used the word reflexive but his results are equivalent to say that every normal operator is reflexive. The word reflexive was suggested by HALMOS and first appeared in H. Rajdavi and P. Rosenthals book `Invariant Subspaces’ in 1973. This line of research was continued by Deddens who showed that every isometry in B(H) is reflexive. R. Wogen has proved that `every quasi-normal operator is reflexive’. These results of Deddens, Sarason, Wogen are particular cases of theorem of Olin and Thomson which says that all sub-normal operators are reflexive. In other direction, Deddens and Fillmore characterized these operators acting on a finite dimensional space are reflexive. J. B. Conway and Dudziak generalized the result of reflexivity of normal, quasi-normal, sub-normal operators by proving the reflexivity of Vonneumann operators. In this paper we shall discuss the condition under which m-isometries operators turned to be reflexive.

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