scholarly journals Factorizations of some lower triangular matrices and related combinatorial identities

2021 ◽  
Vol 27 (4) ◽  
pp. 207-218
Author(s):  
Cahit Köme ◽  
Keyword(s):  
Second Order ◽  
Combinatorial Identities ◽  
Triangular Matrices ◽  
Pascal Matrix ◽  
Lower Triangular ◽  
Lower Triangular Matrices

In this study, we investigate the connection between second order recurrence matrix and several combinatorial matrices such as generalized r-eliminated Pascal matrix, Stirling matrix of the first and of the second kind matrices. We give factorizations and inverse factorizations of these matrices by virtue of the second order recurrence matrix. Moreover, we derive several combinatorial identities which are more general results of some earlier works.

scholarly journals Some subordination involving polynomials induced by lower triangular matrices

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Saiful R. Mondal ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad
Keyword(s):  
Unit Disk ◽  
Triangular Matrices ◽  
Cesàro Mean ◽  
Cesaro Mean ◽  
Lower Triangular ◽  
Lower Triangular Matrices

Abstract The article considers several polynomials induced by admissible lower triangular matrices and studies their subordination properties. The concept generalizes the notion of stable functions in the unit disk. Several illustrative examples, including those related to the Cesàro mean, are discussed, and connections are made with earlier works.

REALIZATION OF FRT ALGEBRA RELATED TO A COLORED BRAID GROUP REPRESENTATION

1994 ◽  
Vol 09 (29) ◽  
pp. 2733-2743 ◽  
Author(s):  
B. BASU-MALLICK
Keyword(s):  
Braid Group ◽  
Group Representation ◽  
Toda Chain ◽  
Baxter Equation ◽  
Color Parameter ◽  
Triangular Matrices ◽  
Explicit Realization ◽  
Lower Triangular ◽  
Parameter Dependent ◽  
Lower Triangular Matrices

A colored braid group representation (CBGR) is constructed by using some modified universal ℛ-matrix associated with U q( gl (2)) quantized algebra. Explicit realization of Faddeev–Reshetikhin–Takhtajan (FRT) algebra, involving color parameter dependent upper and lower triangular matrices, is built up for this CBGR and subsequently applied to generate nonadditive type solutions of quantum Yang–Baxter equation. Rational limit of such solutions interestingly yields 'colored' extension of known Lax operators associated with lattice nonlinear Schrödinger model and Toda chain.

scholarly journals Quasi-nilpotency of Generalized Volterra Operators on Sequence Spaces

2021 ◽  
Vol 76 (4) ◽  
Author(s):  
N. Chalmoukis ◽  
G. Stylogiannis
Keyword(s):  
Volterra Operator ◽  
Sequence Spaces ◽  
Triangular Matrices ◽  
Schur Multipliers ◽  
Taylor Coefficients ◽  
New Class ◽  
Volterra Operators ◽  
Analytic Symbol ◽  
Lower Triangular ◽  
Lower Triangular Matrices

AbstractWe study the quasi-nilpotency of generalized Volterra operators on spaces of power series with Taylor coefficients in weighted $$\ell ^p$$ ℓ p spaces $$1<p<+\infty $$ 1 < p < + ∞ . Our main result is that when an analytic symbol g is a multiplier for a weighted $$\ell ^p$$ ℓ p space, then the corresponding generalized Volterra operator $$T_g$$ T g is bounded on the same space and quasi-nilpotent, i.e. its spectrum is $$\{0\}.$$ { 0 } . This improves a previous result of A. Limani and B. Malman in the case of sequence spaces. Also combined with known results about multipliers of $$\ell ^p$$ ℓ p spaces we give non trivial examples of bounded quasi-nilpotent generalized Volterra operators on $$\ell ^p$$ ℓ p . We approach the problem by introducing what we call Schur multipliers for lower triangular matrices and we construct a family of Schur multipliers for lower triangular matrices on $$\ell ^p, 1<p<\infty $$ ℓ p , 1 < p < ∞ related to summability kernels. To demonstrate the power of our results we also find a new class of Schur multipliers for Hankel operators on $$\ell ^2 $$ ℓ 2 , extending a result of E. Ricard.

A note on cosine series with coefficients of generalized bounded variation

2020 ◽  
Vol 70 (3) ◽  
pp. 681-688
Author(s):  
Bhikha Lila Ghodadra ◽  
Vanda Fülöp
Keyword(s):  
Bounded Variation ◽  
Tauberian Theorem ◽  
Tauberian Theorems ◽  
Weighted Mean ◽  
Triangular Matrices ◽  
Cosine Series ◽  
Lower Triangular ◽  
Hausdorff Matrices ◽  
Lower Triangular Matrices

AbstractIn this note, we obtain a Tauberian theorem for a class of regular lower triangular matrices operating on cosine series with coefficients tending to zero. As corollaries we obtain Tauberian theorems for weighted mean, Nörlund, and Hausdorff matrices.

Sign in / Sign up

Export Citation Format

Share Document