On a Riesz Basis of Finite-Dimensional Invariant Subspaces

2021 ◽  
pp. 255-302
Author(s):  
Aref Jeribi
Keyword(s):  
Riesz Basis ◽  
Invariant Subspaces ◽  
Finite Dimensional

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.

Vector Spaces

2021 ◽  
pp. 47-102
Author(s):  
Adel N. Boules
Keyword(s):  
Invariant Subspaces ◽  
Extensive Study ◽  
Vector Spaces ◽  
Inner Product ◽  
Product Spaces ◽  
Direct Sums ◽  
Infinite Dimensional ◽  
Quotient Spaces ◽  
Inner Product Spaces ◽  
Finite Dimensional

The first three sections of this chapter provide a thorough presentation of the concepts of basis and dimension. The approach is unified in the sense that it does not treat finite and infinite-dimensional spaces separately. Important concepts such as algebraic complements, quotient spaces, direct sums, projections, linear functionals, and invariant subspaces make their first debut in section 3.4. Section 3.5 is a brief summary of matrix representations and diagonalization. Then the chapter introduces normed linear spaces followed by an extensive study of inner product spaces. The presentation of inner product spaces in this section and in section 4.10 is not limited to finite-dimensional spaces but rather to the properties of inner products that do not require completeness. The chapter concludes with the finite-dimensional spectral theory.

scholarly journals Besselian g-frames and near g-Riesz bases

2011 ◽  
Vol 5 (2) ◽  
pp. 259-270 ◽  
Author(s):  
M.R. Abdollahpour ◽  
A. Najati
Keyword(s):  
Hilbert Space ◽  
Riesz Basis ◽  
Orthonormal Basis ◽  
Inner Product ◽  
Riesz Bases ◽  
Finite Dimensional

In this paper we introduce and study near g-Riesz basis, Besselian g-frames and unconditional g-frames. We show that a near g-Riesz basis is a Besselian g-frame and we conclude that under some conditions the kernel of associated synthesis operator for a near g-Riesz basis is finite dimensional. Finally, we show that a g-frame is a g-Riesz basis for a Hilbert space H if and only if there is an equivalent inner product on H, with respect to which it becomes an g-orthonormal basis for H.

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