The diagonal representation of the grunsky operator

1987 ◽  
Vol 9 (1) ◽  
pp. 23-30
Author(s):  
A.. Hinkkanen
Keyword(s):  
Grunsky Operator ◽  
Diagonal Representation

Autoencoder-Based Latent Block-Diagonal Representation for Subspace Clustering

2020 ◽  
pp. 1-11
Author(s):  
Yesong Xu ◽  
Shuo Chen ◽  
Jun Li ◽  
Zongyan Han ◽  
Jian Yang
Keyword(s):  
Subspace Clustering ◽  
Diagonal Representation ◽  
Block Diagonal

scholarly journals Representation of doubly infinite matrices as non-commutative Laurent series

2017 ◽  
Vol 5 (1) ◽  
pp. 250-257 ◽  
Author(s):  
María Ivonne Arenas-Herrera ◽  
Luis Verde-Star
Keyword(s):  
Laurent Series ◽  
Infinite Matrices ◽  
General Properties ◽  
Hessenberg Matrices ◽  
Diagonal Representation

Abstract We present a new way to deal with doubly infinite lower Hessenberg matrices based on the representation of the matrices as the sum of their diagonal submatrices. We show that such representation is a simple and useful tool for computation purposes and also to obtain general properties of the matrices related with inversion, similarity, commutativity, and Pincherle derivatives. The diagonal representation allows us to consider the ring of doubly infinite lower Hessenberg matrices over a ring R as a ring of Laurent series in one indeterminate, with coefficients in the ring of R-valued sequences that don’t commute with the indeterminate.

The grunsky operator and coefficient differences

1997 ◽  
Vol 33 (1-4) ◽  
pp. 113-127 ◽  
Author(s):  
A. Z. Grinshpan ◽  
Ch. Pommerenke
Keyword(s):  
Grunsky Operator

scholarly journals QUANTUM MECHANICS ON A CLOSED LOOP

1994 ◽  
Vol 09 (02) ◽  
pp. 143-150 ◽  
Author(s):  
Y. OHNUKI ◽  
S. KITAKADO
Keyword(s):  
Quantum Mechanics ◽  
Arbitrary Shape ◽  
Closed Loop ◽  
Dirac Quantization ◽  
Diagonal Representation ◽  
Representation Spaces ◽  
Explicit Expressions

Quantum mechanics on the loop of arbitrary shape is formulated, which is an extension of previous formulations of quantum mechanics on S1 preserving its topology. It is shown that the representation spaces of the algebra do not change under the extension. We also derive, in the x-diagonal representation, the explicit expressions for the operators px and py that satisfy the constraints of the Dirac quantization on the closed loop.

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