A new proof of theorem of Toeplitz in summability theory.
Antosik, P., Srinivasan, V.K. (1987)
International Journal of Mathematics and Mathematical Sciences
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Antosik, P., Srinivasan, V.K. (1987)
International Journal of Mathematics and Mathematical Sciences
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Maddox, I.J. (1980)
International Journal of Mathematics and Mathematical Sciences
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Daniel J. Fleming (1987)
Mathematische Zeitschrift
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Titus Hilberdink (2006)
Acta Arithmetica
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Choudhary, B., Mishra, S.K. (1995)
International Journal of Mathematics and Mathematical Sciences
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Yousong Luo, Robin Hill (2015)
Special Matrices
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In this paper we describe some properties of companion matrices and demonstrate some special patterns that arisewhen a Toeplitz or a Hankel matrix is multiplied by a related companion matrix.We present a necessary and sufficient condition, generalizing known results, for a matrix to be the transforming matrix for a similarity between a pair of companion matrices. A special case of our main result shows that a Toeplitz or a Hankel matrix can be extended using associated companion matrices,...
P. Erdös, G. Piranian (1964)
Mathematische Zeitschrift
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Il'in, S.N. (2004)
Zapiski Nauchnykh Seminarov POMI
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A.K. Abdikalykov, V.N. Chugunov, Kh.D. Ikramov (2015)
Special Matrices
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Our motivation was a paper of 1991 indicating three special unitary matrices that map Hermitian Toeplitz matrices by similarity into real Toeplitz-plus-Hankel matrices. Generalizing this result, we give a complete description of unitary similarity automorphisms of the space of Toeplitz-plus-Hankel matrices.
E.H. BAREISS (1969)
Numerische Mathematik
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A. Ohashi, T. Sogabe, T.S. Usuda (2015)
Special Matrices
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We consider a k-tridiagonal ℓ-Toeplitz matrix as one of generalizations of a tridiagonal Toeplitz matrix. In the present paper, we provide a decomposition of the matrix under a certain condition. By the decomposition, the matrix is easily analyzed since one only needs to analyze the small matrix obtained from the decomposition. Using the decomposition, eigenpairs and arbitrary integer powers of the matrix are easily shown as applications.
Boettcher, A., Grudsky, S.M., Silbermann, B. (1997)
The New York Journal of Mathematics [electronic only]
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Z.U. Ahmad, Mursaleen (1987)
Publications de l'Institut Mathématique
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Elżbieta Król-Klimkowska, Marek Ptak (2016)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
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The investigation of properties of generalized Toeplitz operators with respect to the pairs of doubly commuting contractions (the abstract analogue of classical two variable Toeplitz operators) is proceeded. We especially concentrate on the condition of existence such a non-zero operator. There are also presented conditions of analyticity of such an operator.
Huckle, Thomas K., Noutsos, Dimitrios (2007)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
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