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Heller, Katherine C.

doi:10.1016/j.jmaa.2012.05.006

Cited by 14 publications

(10 citation statements)

References 13 publications

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“…In the case of S 2 , the proofs are nearly identical to those just given for D except for the fact that the kernel functions take a slightly different form in S 2 ; for a reference we point the reader to [9]. Notice also that the hypotheses of Lemma 3.3 are slightly altered.…”

Section: Theorem 32mentioning

confidence: 84%

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Compact differences of composition operators on weighted Dirichlet spaces

2014

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Here we consider when the difference of two composition operators is compact on the weighted Dirichlet spaces D α . Specifically we study differences of composition operators on the Dirichlet space D and S 2 , the space of analytic functions whose first derivative is in H 2 , and then use Calderón's complex interpolation to extend the results to the general weighted Dirichlet spaces. As a corollary we consider composition operators induced by linear fractional self-maps of the disk. MSC:47B33, 46E20, 47B32

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Section: Theorem 32mentioning

confidence: 84%

“…however, we cannot identify this sum as an elementary function; for more on this, see [9]. We will discuss how to overcome this obstacle shortly.…”

Section: Spaces Of Analytic Functionsmentioning

confidence: 99%

Compact differences of composition operators on weighted Dirichlet spaces

2014

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“…Heller [14] found a concrete formula for the adjoint C * ϕr on S 2 (D) which involves a compact perturbation. This fact leads to a related universal operator.…”

Section: Universality Of the Adjoint C * ϕ − λI On S 2 (D)mentioning

confidence: 99%

“…Finally, note that the annulus A r is preserved by complex conjugation, so that we may above change C * ϕr − λI to C * ϕr − λI. Heller [14] found a concrete formula for the adjoint C * ϕr on S 2 (D) which involves a compact perturbation. This fact leads to a related universal operator.…”

Section: Structure Of the Class Of Universal Operatorsmentioning

confidence: 99%

On Universal Operators and Universal Pairs

Schroderus¹,

Tylli²

2018

Proceedings of the Edinburgh Mathematical Society

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“…The special case where ϕ is an inner function was discussed earlier in [20]. Recently Heller [16] also found a formula for C * ϕ on the space S 2 (D) for a linear fractional symbol ϕ; here S 2 (D) consists of functions whose derivatives belong to H 2 (D). There are some extensions of these results to composition operators on holomorphic spaces of several variables, for example, see Cowen and MacCluer [9].…”

mentioning

confidence: 98%