One-Component Inner Functions II

Mortini, Raymond; Cima, Joseph A.

doi:10.1007/978-3-030-40120-7_2

Cited by 8 publications

(11 citation statements)

References 10 publications

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“…On the other hand, also as an application of Theorem 6, we construct discrete measures whose associated singular inner functions are not one‐component. Theorem 6 also implies the following result which provides an affirmative answer to another question of Cima and Mortini [11, (Question 4.4 i)]. Corollary Let

E

be a closed countable set of the unit circle.…”

Section: Introduction and Main Resultsmentioning

confidence: 63%

“…Theorem 4 implies also a negative answer to the following question posed in [11] by Cima and Mortini: Is the singular set of any inner function in

I_{c}

necessarily countable?…”

Section: Introduction and Main Resultsmentioning

confidence: 98%

“…As a byproduct he proved also a strong form of the Schwarz–Pick lemma for inner functions in

I_{c}

. Using Aleksandrov's descriptions, Cima, Mortini and the second author constructed some concrete examples of one‐component inner functions [10, 11, 23]. In particular singular inner functions associated to a finite sum of weighted Dirac masses are one‐component and thin Blaschke products are not in

I_{c}

.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

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A characterization of one‐component inner functions

Nicolau

Reijonen

2020

Bull. London Math. Soc.

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We present a characterization of one-component inner functions in terms of the location of their zeros and their associated singular measure. As consequence we answer several questions posed by Cima and Mortini. In particular, we prove that for any inner function Θ whose singular set has measure zero, one can find a Blaschke product B such that BΘ is one-component. We also obtain a characterization of one-component singular inner functions which is used to produce examples of discrete and continuous one-component singular inner functions.

show abstract

E

be a closed countable set of the unit circle.…”

Section: Introduction and Main Resultsmentioning

confidence: 63%

“…Theorem 4 implies also a negative answer to the following question posed in [11] by Cima and Mortini: Is the singular set of any inner function in

I_{c}

necessarily countable?…”

Section: Introduction and Main Resultsmentioning

confidence: 98%

“…As a byproduct he proved also a strong form of the Schwarz–Pick lemma for inner functions in

I_{c}

I_{c}

.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

See 1 more Smart Citation

A characterization of one‐component inner functions

Nicolau

Reijonen

2020

Bull. London Math. Soc.

View full text Add to dashboard Cite

show abstract

“…Theorem 4 implies also a negative answer to the following question posed in [11] by J. Cima and R. Mortini: Is the singular set of any inner function in I c necessarily countable?…”

Section: Introduction and Main Resultsmentioning

confidence: 98%

“…As a byproduct he proved also a strong form of the Schwarz-Pick lemma for inner functions in I c . Using Aleksandrov's descriptions, J. Cima, R. Mortini and the second author constructed some concrete examples of one-component inner functions [10,11,23]. In particular singular inner functions associated to a finite sum of weighted Dirac masses are one-component and thin Blaschke products are not in I c .…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

A Characterization of One-component Inner Functions

Nicolau,

Reijonen

2020

Preprint

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We present a characterization of one-component inner functions in terms of the location of their zeros and their associated singular measure. As consequence we answer several questions posed by J. Cima and R. Mortini. In particular we prove that for any inner function Θ whose singular set has measure zero, one can find a Blaschke product B such that ΘB is one-component. We also obtain a characterization of one-component singular inner functions which is used to produce examples of discrete and continuous one-component singular inner functions.

show abstract

Truncated Toeplitz Operators

Fricain

2023

Fields Institute Monographs

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One-Component Inner Functions II

Cited by 8 publications

References 10 publications

A characterization of one‐component inner functions

A characterization of one‐component inner functions

A Characterization of One-component Inner Functions

Truncated Toeplitz Operators

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