Kernels of a Class of Toeplitz Plus Hankel Operators with Piecewise Continuous Generating Functions

2018 ◽  
pp. 317-337 ◽  
Author(s):  
Victor D. Didenko ◽  
Bernd Silbermann
Keyword(s):  
Generating Functions ◽  
Hankel Operators ◽  
Piecewise Continuous

Hankel operators with PC symbols and the space H∞ + PC

1981 ◽  
Vol 89 (1-2) ◽  
pp. 17-24 ◽  
Author(s):  
F. F. Bonsall ◽  
T. A. Gillespie
Keyword(s):  
Unit Circle ◽  
Explicit Formula ◽  
Hardy Spaces ◽  
Hankel Operator ◽  
Essential Norm ◽  
Hankel Operators ◽  
Continuous Functions ◽  
Piecewise Continuous ◽  
The Way

SynopsisWe obtain an explicit formula for the essential norm of a Hankel operator with its symbol in the space PC, which is the closure in L∞ of the space of piecewise continuous functions on the unit circle . It follows from this formula that functions in PC can be approximated as closely by functions in C, the continuous functions on the circle, as by functions in the much larger space H∞ + C. This is an example of the way in which properties of the Hardy spaces can be derived from properties of Hankel operators.

scholarly journals The Coburn-Simonenko theorem for some classes of Wiener-Hopf plus Hankel operators

2014 ◽  
Vol 96 (110) ◽  
pp. 85-102 ◽  
Author(s):  
Victor Didenko ◽  
Bernd Silbermann
Keyword(s):  
Generating Functions ◽  
Hankel Operators ◽  
Matching Condition ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
R Functions

Wiener-Hopf plus Hankel operators W(a)+ H(b) : Lp(R+) ? Lp(R+) with generating functions a and b from a subalgebra of L?(R) containing almost periodic functions and Fourier images of L1(R)-functions are studied. For a and b satisfying the so-called matching condition a(t)a(?t) = b(t)b(?t), t ? R, we single out some classes of operators W(a)+ H(b) which are subject to the Coburn-Simonenko theorem.

scholarly journals The Spectral Density of Hankel Operators with Piecewise Continuous Symbols

2019 ◽  
Vol 92 (1) ◽  
Author(s):  
Emilio Fedele
Keyword(s):  
Asymptotic Formula ◽  
Spectral Density ◽  
Unit Circle ◽  
Hankel Operators ◽  
Continuous Functions ◽  
Hankel Matrices ◽  
Triangular Truncation ◽  
Distribution Of Eigenvalues ◽  
Hilbert Matrix ◽  
Piecewise Continuous

AbstractIn 1966, H. Widom proved an asymptotic formula for the distribution of eigenvalues of the $$N\times N$$N×N truncated Hilbert matrix for large values of N. In this paper, we extend this formula to Hankel matrices with symbols in the class of piece-wise continuous functions on the unit circle. Furthermore, we show that the distribution of the eigenvalues is independent of the choice of truncation (e.g. square or triangular truncation).

Operators induced by weighted Toeplitz and weighted Hankel operators

2018 ◽  
Vol 48 (2) ◽  
pp. 99-111
Author(s):  
Gopal Datt ◽  
Anshika Mittal
Keyword(s):  
Hankel Operators

Short Generating Functions for some Semigroup Algebras

10.37236/1729 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Graham Denham
Keyword(s):  
Rational Function ◽  
Generating Functions ◽  
Hilbert Series ◽  
Simple Expression ◽  
Arbitrary Field ◽  
Graded Algebra ◽  
Semigroup Algebras ◽  
Positive Integers

Let $a_1,\ldots,a_n$ be distinct, positive integers with $(a_1,\ldots,a_n)=1$, and let k be an arbitrary field. Let $H(a_1,\ldots,a_n;z)$ denote the Hilbert series of the graded algebra k$[t^{a_1},t^{a_2},\ldots,t^{a_n}]$. We show that, when $n=3$, this rational function has a simple expression in terms of $a_1,a_2,a_3$; in particular, the numerator has at most six terms. By way of contrast, it is known that no such expression exists for any $n\geq4$.

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