Necessary and sufficient conditions for the invertibility of the non-linear difference operator $ (\mathscr Dx)(t)=x(t+1)-f(x(t))$ in the space of bounded continuous functions on the real axis

2001 ◽  
Vol 192 (4) ◽  
pp. 565-576 ◽  
Author(s):  
V E Slyusarchuk
Keyword(s):  
Real Axis ◽  
Difference Operator ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Necessary And Sufficient Conditions ◽  
The Real ◽  
Linear Difference Operator ◽  
Non Linear ◽  
Necessary And Sufficient ◽  
Bounded Continuous Functions

A Subnormal Operator and its Dual

1996 ◽  
Vol 48 (2) ◽  
pp. 381-396
Author(s):  
Robert F. Olin ◽  
Liming Yang
Keyword(s):  
Unit Circle ◽  
Essential Spectrum ◽  
Real Axis ◽  
Additional Assumption ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Subnormal Operator ◽  
The Real ◽  
Necessary And Sufficient

AbstractIt is shown that the essential spectrum of a cyclic, self-dual, subnormal operator is symmetric with respect to the real axis. The study of the structure of a cyclic, irreducible, self-dual, subnormal operator is reduced to the operator Sμ with bpeμ = D. Necessary and sufficient conditions for a cyclic subnormal operator Sμ with bpeμ = D to be self-dual are obtained under the additional assumption that the measure on the unit circle is log-integrable. Finally, an approach to a general cyclic, self-dual, subnormal operator is discussed.

ON PROJECTIVELY RELATED WARPED PRODUCT FINSLER MANIFOLDS

2011 ◽  
Vol 08 (05) ◽  
pp. 953-967 ◽  
Author(s):  
M. M. REZAII ◽  
Y. ALIPOUR-FAKHRI
Keyword(s):  
Warped Product ◽  
Sufficient Conditions ◽  
Linear Connection ◽  
Necessary And Sufficient Conditions ◽  
Finsler Manifolds ◽  
Non Linear ◽  
Necessary And Sufficient

Let 𝔽1 = (M1,F1) and 𝔽2 = (M2,F2) be two Finsler manifolds and let M = M1 × M2 and S is a spray in M. Also 𝔽 = (M1 × f M2, F) is a warped product Finsler manifolds, such that the function f : M1 → ℝ+ is not constant. In this paper, we define a non-linear connection on warped product 𝔽, and finally, we have presented some necessary and sufficient conditions under which the spray manifold (M1 × M2, S) is projectively equivalent to the warped product Finsler manifolds (M1 × f M2, F).

Characterizations of symmetric cones by means of the basic relative invariants of homogeneous cones

2016 ◽  
Vol 7 (2) ◽  
Author(s):  
Hideto Nakashima
Keyword(s):  
Sufficient Conditions ◽  
Rational Functions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Symmetric Cones ◽  
The Real ◽  
Tube Domains ◽  
Homogeneous Cone ◽  
Necessary And Sufficient ◽  
Relative Invariants

AbstractIn this paper, we give necessary and sufficient conditions for a homogeneous cone Ω to be symmetric in two ways. One is by using the multiplier matrix of Ω, and the other is in terms of the basic relative invariants of Ω. In the latter approach, we need to show that the real parts of certain meromorphic rational functions obtained by the basic relative invariants are always positive on the tube domains over Ω. This is a generalization of a result of Ishi and Nomura [Math. Z. 259 (2008), 604–674].

A theorem of Stone-Weierstrass type

1966 ◽  
Vol 62 (4) ◽  
pp. 649-666 ◽  
Author(s):  
G. A. Reid
Keyword(s):  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Necessary And Sufficient Conditions ◽  
Weierstrass Theorem ◽  
Necessary And Sufficient ◽  
Complex Valued

The Stone-Weierstrass theorem gives very simple necessary and sufficient conditions for a subset A of the algebra of all real-valued continuous functions on the compact Hausdorff space X to generate a subalgebra dense in namely, this is so if and only if the functions of A strongly separate the points of X, in other words given any two distinct points of X there exists a function in A taking different values at these points, and given any point of X there exists a function in A non-zero there. In the case of the algebra of all complex-valued continuous functions on X, the same result holds provided that we consider the subalgebra generated by A together with Ā, the set of complex conjugates of the functions in A.

Hermite-Fejér interpolation with Jacobi weights

2011 ◽  
Vol 48 (3) ◽  
pp. 408-420
Author(s):  
G. Mastroianni ◽  
J. Szabados
Keyword(s):  
Error Estimates ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Necessary And Sufficient Conditions ◽  
Interpolation Process ◽  
Weighted Norm ◽  
Jacobi Weights ◽  
Jacobi Weight ◽  
Necessary And Sufficient

We consider the weighted Hermite-Fejér interpolation process based on Jacobi nodes for classes of locally continuous functions defined by another Jacobi weight. Necessary and sufficient conditions for the weighted norm boundedness and for the convergence, as well as error estimates of the approximation, are given.

scholarly journals Recurrence classification for a family of non-linear storage models

2018 ◽  
Vol 37 (2) ◽  
pp. 337-353
Author(s):  
Peter W. Glynn ◽  
Sanatan Rai ◽  
John E. Glynn
Keyword(s):  
Discrete Time ◽  
Power Law ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Storage Model ◽  
Positive Recurrence ◽  
Non Linear ◽  
Necessary And Sufficient ◽  
Recurrence Classification

RECURRENCE CLASSIFICATION FOR A FAMILY OF NON-LINEAR STORAGE MODELSNecessary and sufficient conditions for positive recurrence of a discrete-time non-linear storage model with power law dynamics arederived. In addition, necessary and sufficient conditions for finiteness of p-th stationary moments are obtained for this class of models.

scholarly journals On Ψ-instability of non-linear matrix Lyapunov systems

2009 ◽  
Vol 42 (4) ◽  
Author(s):  
M. S. N. Murty ◽  
G. S. Kumar ◽  
P. N. Lakshmi ◽  
D. Anjaneyulu
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Matrix ◽  
Non Linear ◽  
Necessary And Sufficient

AbstractWe prove necessary and sufficient conditions for Ψ-instability of trivial solutions of linear matrix Lyapunov systems and also sufficient conditions for Ψ-instability of trivial solutions of non-linear matrix Lyapunov systems.

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