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Articles 1 - 30 of 94
Full-Text Articles in Physical Sciences and Mathematics
An Unnoticed Consequence Of Szego's Distribution Theorem, William F. Trench
An Unnoticed Consequence Of Szego's Distribution Theorem, William F. Trench
William F. Trench
No abstract provided.
Inverse Problems For Unilevel Block $\Alpha$-Circulants, William F. Trench
Inverse Problems For Unilevel Block $\Alpha$-Circulants, William F. Trench
William F. Trench
No abstract provided.
An Elementary View Of Weyl's Theory Of Equal Distribution, William Trench
An Elementary View Of Weyl's Theory Of Equal Distribution, William Trench
William F. Trench
No abstract provided.
Characterization And Properties Of $(R,S_\Sigma)$-Commutative Matrices, William F. Trench
Characterization And Properties Of $(R,S_\Sigma)$-Commutative Matrices, William F. Trench
William F. Trench
No abstract provided.
Characterization And Properties Of $(R,S_\Sigma)$-Commutative Matrices, William F. Trench
Characterization And Properties Of $(R,S_\Sigma)$-Commutative Matrices, William F. Trench
William F. Trench
Let $R=P \diag(\gamma_{0}I_{m_{0}}, \gamma_{1}I_{m_{1}}, \dots, \gamma_{k-1}I_{m_{k-1}})P^{-1}\in\mathbb{C}^{m\times m}$ and $S_{\sigma}=Q\diag(\gamma_{\sigma(0)}I_{n_{0}},\gamma_{\sigma(1)}I_{n_{1}}, \dots,\gamma_{\sigma(k-1)}I_{n_{k-1}})Q^{-1}\in\mathbb{C}^{n\times n}$, where $m_{0}+m_{1}+\cdots +m_{k-1}=m$, $n_{0}+n_{1}+\cdots+n_{k-1}=n$, $\gamma_{0}$, $\gamma_{1}$, \dots, $\gamma_{k-1}$ are distinct complex numbers, and $\sigma :\mathbb{Z}_{k}\to\mathbb{Z}_{k}= \{0,1, \dots, k-1\}$. We say that $A\in\mathbb{C}^{m\times n}$ is $(R,S_{\sigma})$-commutative if $RA=AS_{\sigma}$. We characterize the class of $(R,S_{\sigma})$-commutative matrrices and extend results obtained previously for the case where $\gamma_{\ell}=e^{2\pi i\ell/k}$ and $\sigma(\ell)=\alpha\ell+\mu \pmod{k}$, $0 \le \ell \le k-1$, with $\alpha$, $\mu\in\mathbb{Z}_{k}$. Our results are independent of $\gamma_{0}$, $\gamma_{1}$, \dots, $\gamma_{k-1}$, so long as they are distinct; i.e., if $RA=AS_{\sigma}$ for some choice of $\gamma_{0}$, $\gamma_{1}$, \dots, $\gamma_{_{k-1}}$ (all distinct), then $RA=AS_{\sigma}$ for arbitrary of …
Asymptotic Preconditioning Of Linear Homogeneous Systems Of Differential Equations, William F. Trench
Asymptotic Preconditioning Of Linear Homogeneous Systems Of Differential Equations, William F. Trench
William F. Trench
No abstract provided.
Characterization And Properties Of Matrices With $K$-Involutory Symmetries Ii, William F. Trench
Characterization And Properties Of Matrices With $K$-Involutory Symmetries Ii, William F. Trench
William F. Trench
No abstract provided.
Properties Of Multilevel Block $\Alpha$-Circulants, William F. Trench
Properties Of Multilevel Block $\Alpha$-Circulants, William F. Trench
William F. Trench
No abstract provided.
On Nonautonomous Linear Systems Of Differential And Difference Equations With $R$-Symmetric Coefficient Matrices, William F. Trench
On Nonautonomous Linear Systems Of Differential And Difference Equations With $R$-Symmetric Coefficient Matrices, William F. Trench
William F. Trench
No abstract provided.
Characterization And Properties Of Matrices With K-Involutory Symmetries, William F. Trench
Characterization And Properties Of Matrices With K-Involutory Symmetries, William F. Trench
William F. Trench
No abstract provided.
Absolute Equal Distribution Of The Eigenvalues Of Discrete Sturm-Liouville Problems, William F. Trench
Absolute Equal Distribution Of The Eigenvalues Of Discrete Sturm-Liouville Problems, William F. Trench
William F. Trench
No abstract provided.
Functional Perturbations Of Nonoscillatory Second Order Difference Equations, William F. Trench
Functional Perturbations Of Nonoscillatory Second Order Difference Equations, William F. Trench
William F. Trench
No abstract provided.
Characterization And Properties Of $(R,S)$-Symmetric, $(R,S)$-Skew Symmetric, And $(R,S)$-Conjugate Matrices, William F. Trench
Characterization And Properties Of $(R,S)$-Symmetric, $(R,S)$-Skew Symmetric, And $(R,S)$-Conjugate Matrices, William F. Trench
William F. Trench
No abstract provided.
Asymptotic Relationships Between Singular Values Of Structured Matrices Similarly Generated By Different Formal Expansions Of A Rational Function, William F. Trench
Asymptotic Relationships Between Singular Values Of Structured Matrices Similarly Generated By Different Formal Expansions Of A Rational Function, William F. Trench
William F. Trench
No abstract provided.
Multilevel Matrices With Involutory Symmetries And Skew Symmetries, William F. Trench
Multilevel Matrices With Involutory Symmetries And Skew Symmetries, William F. Trench
William F. Trench
No abstract provided.
Inverse Eigenproblems And Associated Approximation Problems For Matrices With Generalized Symmetry Or Skew Symmetry, William F. Trench
Inverse Eigenproblems And Associated Approximation Problems For Matrices With Generalized Symmetry Or Skew Symmetry, William F. Trench
William F. Trench
No abstract provided.
Hermitian, Hermitian R-Symmetric, And Hermitian R-Skew Symmetric Procrustes Problems, William F. Trench
Hermitian, Hermitian R-Symmetric, And Hermitian R-Skew Symmetric Procrustes Problems, William F. Trench
William F. Trench
No abstract provided.
Minimization Problems For (R,S)-Symmetric And (R,S)-Skew Symmetric Matrices, William F. Trench
Minimization Problems For (R,S)-Symmetric And (R,S)-Skew Symmetric Matrices, William F. Trench
William F. Trench
No abstract provided.
Simplification And Strengthening Of Weyl's Definition Of Asymptotic Equal Distribution Of Two Families Of Finite Sets, William F. Trench
Simplification And Strengthening Of Weyl's Definition Of Asymptotic Equal Distribution Of Two Families Of Finite Sets, William F. Trench
William F. Trench
No abstract provided.
An Elementary Note On Asymptotic Properties Of Toeplitz And Multilevel Toeplitz Matrices, William F. Trench
An Elementary Note On Asymptotic Properties Of Toeplitz And Multilevel Toeplitz Matrices, William F. Trench
William F. Trench
No abstract provided.
Spectral Distribution Of Hermitian Toeplitz Matrices Formally Generated By Rational Functions, William F. Trench
Spectral Distribution Of Hermitian Toeplitz Matrices Formally Generated By Rational Functions, William F. Trench
William F. Trench
No abstract provided.
A Note On Asymptotic Zero Distribution Of Orthogonal Polynomials, William F. Trench
A Note On Asymptotic Zero Distribution Of Orthogonal Polynomials, William F. Trench
William F. Trench
No abstract provided.
Absolute Equal Distribution Of The Spectra Of Hermitian Matrices, William F. Trench
Absolute Equal Distribution Of The Spectra Of Hermitian Matrices, William F. Trench
William F. Trench
No abstract provided.
Absolute Equal Distribution Of Families Of Finite Sets, William F. Trench
Absolute Equal Distribution Of Families Of Finite Sets, William F. Trench
William F. Trench
No abstract provided.
Linear Perturbations Of A Nonoscillatory Second Order Differential Equation Ii, William F. Trench
Linear Perturbations Of A Nonoscillatory Second Order Differential Equation Ii, William F. Trench
William F. Trench
No abstract provided.
Asymptotically Constant Solutions Of Functional Difference Systems, William F. Trench
Asymptotically Constant Solutions Of Functional Difference Systems, William F. Trench
William F. Trench
No abstract provided.
Properties Of Some Generalizations Of Kac-Murdock-Szeg"O Matrices, William Trench
Properties Of Some Generalizations Of Kac-Murdock-Szeg"O Matrices, William Trench
William F. Trench
No abstract provided.
Systems Of Difference Equations With Asymptotically Constant Solutions, William F. Trench
Systems Of Difference Equations With Asymptotically Constant Solutions, William F. Trench
William F. Trench
No abstract provided.
Conditional Convergence Of Infinite Products, William F. Trench
Conditional Convergence Of Infinite Products, William F. Trench
William F. Trench
No abstract provided.
Linear Asymptotic Equilibrium For Nilpotent Systems Of Difference Equations, William F. Trench
Linear Asymptotic Equilibrium For Nilpotent Systems Of Difference Equations, William F. Trench
William F. Trench
No abstract provided.