Open Access. Powered by Scholars. Published by Universities.®
- Discipline
- Keyword
-
- Infinite order differential operators (2)
- Amenable groups (1)
- Appell system (1)
- Ergodic Ramsey theory (1)
- Ergodic Roth theorem (1)
-
- Fock space (1)
- Fueter mapping (1)
- Furstenberg correspondence principle (1)
- Generalized functions (1)
- Hardy space (1)
- Hypercomplex derivative (1)
- Quaternions (1)
- Reproducing kernels (1)
- Schrödinger equation (1)
- Shift operator (1)
- Superoscillations (1)
- Superoscillatory functions (1)
- Supershifts in several variables (1)
- Syndetic sets (1)
- Uncountable ergodic theory (1)
- Uniformity in recurrence (1)
Articles 1 - 5 of 5
Full-Text Articles in Other Mathematics
An Uncountable Ergodic Roth Theorem And Applications, Polona Durcik, Rachel Greenfeld, Annina Iseli, Asgar Jamneshan, José Madrid
An Uncountable Ergodic Roth Theorem And Applications, Polona Durcik, Rachel Greenfeld, Annina Iseli, Asgar Jamneshan, José Madrid
Mathematics, Physics, and Computer Science Faculty Articles and Research
We establish an uncountable amenable ergodic Roth theorem, in which the acting group is not assumed to be countable and the space need not be separable. This generalizes a previous result of Bergelson, McCutcheon and Zhang, and complements a result of Zorin- Kranich. We establish the following two additional results: First, a combinatorial application about triangular patterns in certain subsets of the Cartesian square of arbitrary amenable groups, extending a result of Bergelson, McCutcheon and Zhang for countable amenable groups. Second, a uniformity aspect in the double recurrence theorem for Γ-systems for arbitrary uniformly amenable groups Γ. Our uncountable Roth …
On Superoscillations And Supershifts In Several Variables, Yakir Aharonov, Fabrizio Colombo, Andrew N. Jordan, Irene Sabadini, Tomer Shushi, Daniele C. Struppa, Jeff Tollaksen
On Superoscillations And Supershifts In Several Variables, Yakir Aharonov, Fabrizio Colombo, Andrew N. Jordan, Irene Sabadini, Tomer Shushi, Daniele C. Struppa, Jeff Tollaksen
Mathematics, Physics, and Computer Science Faculty Articles and Research
The aim of this paper is to study a class of superoscillatory functions in several variables, removing some restrictions on the functions that we introduced in a previous paper. Since the tools that we used with our approach are not common knowledge we will give detailed proof for the case of two variables. The results proved for superoscillatory functions in several variables can be further extended to supershifts in several variables.
Fock And Hardy Spaces: Clifford Appell Case, Daniel Alpay, Kamal Diki, Irene Sabadini
Fock And Hardy Spaces: Clifford Appell Case, Daniel Alpay, Kamal Diki, Irene Sabadini
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper, we study a specific system of Clifford–Appell polynomials and, in particular, their product. Moreover, we introduce a new family of quaternionic reproducing kernel Hilbert spaces in the framework of Fueter regular functions. The construction is based on a general idea which allows us to obtain various function spaces by specifying a suitable sequence of real numbers. We focus on the Fock and Hardy cases in this setting, and we study the action of the Fueter mapping and its range.
Superoscillating Sequences And Supershifts For Families Of Generalized Functions, F. Colombo, I. Sabadini, Daniele Carlo Struppa, A. Yger
Superoscillating Sequences And Supershifts For Families Of Generalized Functions, F. Colombo, I. Sabadini, Daniele Carlo Struppa, A. Yger
Mathematics, Physics, and Computer Science Faculty Articles and Research
We construct a large class of superoscillating sequences, more generally of F-supershifts, where F is a family of smooth functions in (t, x) (resp. distributions in (t, x), or hyperfunctions in x depending on the parameter t) indexed by λ ∈ R. The frame in which we introduce such families is that of the evolution through Schrödinger equation (i∂/∂t−H (x))(ψ) = 0 (H (x) = −(∂2/∂x2)/2+V (x)), V being a suitable potential). If F = {(t, x) → ϕλ(t, x) ; λ ∈ R}, where ϕλ is evolved from the initial datum x → eiλx , F-supershifts will be of …
Boundedness Of Some Multi-Parameter Fiber-Wise Multiplier Operators, Frédéric Bernicot, Polona Durcik
Boundedness Of Some Multi-Parameter Fiber-Wise Multiplier Operators, Frédéric Bernicot, Polona Durcik
Mathematics, Physics, and Computer Science Faculty Articles and Research
We prove Lp estimates for various multi-parameter bi- and trilinear operators with symbols acting on fibers of the two-dimensional functions. In particular, this yields estimates for the general bi-parameter form of the twisted paraproduct studied in [V. Kovač, Boundedness of the twisted paraproduct. Rev. Mat. Iberoam. 28 (2012), no. 4, 1143–1164.].