Fractional Integrodifferentiation and Toeplitz Operators with Vertical Symbols
We consider the so-called vertical Toeplitz operators on the weighted Bergman space over the half plane. The terminology “vertical” is motivated by the fact that if a is a symbol of such Toeplitz operator, then a(z) depends only on y = ℑz, where z = x + iy. The main question raised in this paper can...
محفوظ في:
| المؤلف الرئيسي: | |
|---|---|
| مؤلفون آخرون: | |
| التنسيق: | bookPart |
| منشور في: |
2020
|
| الموضوعات: | |
| الوصول للمادة أونلاين: | http://hdl.handle.net/11073/25078 |
| الوسوم: |
إضافة وسم
لا توجد وسوم, كن أول من يضع وسما على هذه التسجيلة!
|
| _version_ | 1864513442483798016 |
|---|---|
| author | Karapetyants, Alexey |
| author2 | Louhichi, Issam |
| author2_role | author |
| author_facet | Karapetyants, Alexey Louhichi, Issam |
| author_role | author |
| dc.creator.none.fl_str_mv | Karapetyants, Alexey Louhichi, Issam |
| dc.date.none.fl_str_mv | 2020 2022-11-30T06:44:41Z 2022-11-30T06:44:41Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | Karapetyants, A., Louhichi, I. (2020). Fractional integrodifferentiation and Toeplitz operators with vertical symbols. In: Bauer, W., Duduchava, R., Grudsky, S., Kaashoek, M. (Eds.), Operator Algebras, Toeplitz Operators and Related Topics (pp. 175-187). Birkhäuser. https://doi.org/10.1007/978-3-030-44651-2_13 9783030446512 http://hdl.handle.net/11073/25078 10.1007/978-3-030-44651-2_13 |
| dc.language.none.fl_str_mv | en_US |
| dc.publisher.none.fl_str_mv | Birkhäuser |
| dc.relation.none.fl_str_mv | https://doi.org/10.1007/978-3-030-44651-2_13 |
| dc.subject.none.fl_str_mv | Toepliz operators Riemann-Liouville fractional integrodifferentiation Spaces of holomorphic functions |
| dc.title.none.fl_str_mv | Fractional Integrodifferentiation and Toeplitz Operators with Vertical Symbols |
| dc.type.none.fl_str_mv | Postprint info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/bookPart |
| description | We consider the so-called vertical Toeplitz operators on the weighted Bergman space over the half plane. The terminology “vertical” is motivated by the fact that if a is a symbol of such Toeplitz operator, then a(z) depends only on y = ℑz, where z = x + iy. The main question raised in this paper can be formulated as follows: given two bounded vertical Toeplitz operators Tλa and Tλb, under which conditions is there a symbol h such that TλaTλb=Tλh? It turns out that this problem has a very nice connection with fractional calculus! We shall formulate our main results using the well-known theory of Riemann–Liouville fractional integrodifferentiation. |
| format | bookPart |
| id | aus_77fc63e2a7a83b4f449d5f4f968996b5 |
| identifier_str_mv | Karapetyants, A., Louhichi, I. (2020). Fractional integrodifferentiation and Toeplitz operators with vertical symbols. In: Bauer, W., Duduchava, R., Grudsky, S., Kaashoek, M. (Eds.), Operator Algebras, Toeplitz Operators and Related Topics (pp. 175-187). Birkhäuser. https://doi.org/10.1007/978-3-030-44651-2_13 9783030446512 10.1007/978-3-030-44651-2_13 |
| language_invalid_str_mv | en_US |
| network_acronym_str | aus |
| network_name_str | aus |
| oai_identifier_str | oai:repository.aus.edu:11073/25078 |
| publishDate | 2020 |
| publisher.none.fl_str_mv | Birkhäuser |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | Fractional Integrodifferentiation and Toeplitz Operators with Vertical SymbolsKarapetyants, AlexeyLouhichi, IssamToepliz operatorsRiemann-Liouville fractional integrodifferentiationSpaces of holomorphic functionsWe consider the so-called vertical Toeplitz operators on the weighted Bergman space over the half plane. The terminology “vertical” is motivated by the fact that if a is a symbol of such Toeplitz operator, then a(z) depends only on y = ℑz, where z = x + iy. The main question raised in this paper can be formulated as follows: given two bounded vertical Toeplitz operators Tλa and Tλb, under which conditions is there a symbol h such that TλaTλb=Tλh? It turns out that this problem has a very nice connection with fractional calculus! We shall formulate our main results using the well-known theory of Riemann–Liouville fractional integrodifferentiation.Fulbright Outreach Lecturing FundRussian Foundation for Fundamental ResearchBirkhäuser2022-11-30T06:44:41Z2022-11-30T06:44:41Z2020Postprintinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/bookPartapplication/pdfKarapetyants, A., Louhichi, I. (2020). Fractional integrodifferentiation and Toeplitz operators with vertical symbols. In: Bauer, W., Duduchava, R., Grudsky, S., Kaashoek, M. (Eds.), Operator Algebras, Toeplitz Operators and Related Topics (pp. 175-187). Birkhäuser. https://doi.org/10.1007/978-3-030-44651-2_139783030446512http://hdl.handle.net/11073/2507810.1007/978-3-030-44651-2_13en_UShttps://doi.org/10.1007/978-3-030-44651-2_13oai:repository.aus.edu:11073/250782024-08-22T12:02:00Z |
| spellingShingle | Fractional Integrodifferentiation and Toeplitz Operators with Vertical Symbols Karapetyants, Alexey Toepliz operators Riemann-Liouville fractional integrodifferentiation Spaces of holomorphic functions |
| status_str | publishedVersion |
| title | Fractional Integrodifferentiation and Toeplitz Operators with Vertical Symbols |
| title_full | Fractional Integrodifferentiation and Toeplitz Operators with Vertical Symbols |
| title_fullStr | Fractional Integrodifferentiation and Toeplitz Operators with Vertical Symbols |
| title_full_unstemmed | Fractional Integrodifferentiation and Toeplitz Operators with Vertical Symbols |
| title_short | Fractional Integrodifferentiation and Toeplitz Operators with Vertical Symbols |
| title_sort | Fractional Integrodifferentiation and Toeplitz Operators with Vertical Symbols |
| topic | Toepliz operators Riemann-Liouville fractional integrodifferentiation Spaces of holomorphic functions |
| url | http://hdl.handle.net/11073/25078 |