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Physical Sciences and Mathematics Commons™
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- Canonical systems (3)
- Siegel upper half space (2)
- Absolutely continuous spectrum (1)
- Active Learning (1)
- Almost periodic functions (1)
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- Calculus (1)
- De Branges theorem (1)
- Differential equations (1)
- Discrete Schrödinger equation (1)
- Finsler metric (1)
- Flipped Classroom (1)
- Hilbert space (1)
- Limit circle (1)
- Limit point (1)
- Linear relations (1)
- Reflectionless Hamiltonians (1)
- Self-adjoint relations (1)
- Spectral theory (1)
- Symplectic matrix (1)
- Theoretical mathematics (1)
- Titchmarsh-Weyl m-function (1)
- Weyl disk (1)
- Weyl-m function (1)
- Weyl-m functions (1)
Articles 1 - 9 of 9
Full-Text Articles in Physical Sciences and Mathematics
Transitioning To An Active Learning Environment For Calculus At The University Of Florida, Darryl Chamberlain, Amy Grady, Scott Keeran, Kevin Knudson, Ian Manly, Melissa Shabazz, Corey Stone
Transitioning To An Active Learning Environment For Calculus At The University Of Florida, Darryl Chamberlain, Amy Grady, Scott Keeran, Kevin Knudson, Ian Manly, Melissa Shabazz, Corey Stone
Publications
In this note, we describe a large-scale transition to an active learning format in first-semester calculus at the University of Florida. Student performance and attitudes are compared across traditional lecture and flipped sections.
Titchmarsh–Weyl Theory For Vector-Valued Discrete Schrödinger Operators, Keshav R. Acharya
Titchmarsh–Weyl Theory For Vector-Valued Discrete Schrödinger Operators, Keshav R. Acharya
Publications
We develop the Titchmarsh–Weyl theory for vector-valued discrete Schrödinger operators. We show that the Weyl m functions associated with these operators are matrix valued Herglotz functions that map complex upper half plane to the Siegel upper half space. We discuss about the Weyl disk and Weyl circle corresponding to these operators by defining these functions on a bounded interval. We also discuss the geometric properties of Weyl disk and find the center and radius of the Weyl disk explicitly in terms of matrices.
Action Of Complex Symplectic Matrices On The Siegel Upper Half Space, Keshav R. Acharya, Matt Mcbride
Action Of Complex Symplectic Matrices On The Siegel Upper Half Space, Keshav R. Acharya, Matt Mcbride
Publications
The Siegel upper half space, Sn, the space of complex symmetric matrices, Z with positive definite imaginary part, is the generalization of the complex upper half plane in higher dimensions. In this paper, we study a generalization of linear fractional transformations, ΦS, where S is a complex symplectic matrix, on the Siegel upper half space. We partially classify the complex symplectic matrices for which ΦS(Z) is well defined. We also consider Sn and Sn as metric spaces and discuss distance properties of the map ΦS from Sn to Sn and Sn respectively.
A Note On Vector Valued Discrete Schrödinger Operators, Keshav R. Acharya
A Note On Vector Valued Discrete Schrödinger Operators, Keshav R. Acharya
Publications
The main purpose of this paper is to extend some theory of Schrödinger operators from one dimension to higher dimension. In particular, we will give systematic operator theoretic analysis for the Schrödinger equations in multidimensional space. To this end, we will provide the detail proves of some basic results that are necessary for further studies in these areas. In addition, we will introduce Titchmarsh- Weyl m− function of these equations and express m− function in term of the resolvent operators.
Remling's Theorem On Canonical Systems, Keshav R. Acharya
Remling's Theorem On Canonical Systems, Keshav R. Acharya
Publications
In this paper, we extend the Remling’s Theorem on canonical systems that the ω limit points of the Hamiltonian under the shift map are reflectionless on the support of the absolutely continuous part of the spectral measure of a canonical system.
An Alternate Proof Of The De Branges Theorem On Canonical Systems, Keshav R. Acharya
An Alternate Proof Of The De Branges Theorem On Canonical Systems, Keshav R. Acharya
Publications
The aim of this paper is to show that, in the limit circle case, the defect index of a symmetric relation induced by canonical systems, is constant on ₵. This provides an alternative proof of the De Branges theorem that the canonical systems with trH1 imply the limit point case. To this end, we discuss the spectral theory of a linear relation induced by a canonical system.
Self-Adjoint Extension And Spectral Theory Of A Linear Relation In A Hilbert Space, Keshav R. Acharya
Self-Adjoint Extension And Spectral Theory Of A Linear Relation In A Hilbert Space, Keshav R. Acharya
Publications
The aim of this paper is to develop the conditions for a symmetric relation in a Hilbert space ℋ to have self-adjoint extensions in terms of defect indices and discuss some spectral theory of such linear relation.
Titchmarsh-Weyl Theory For Canonical Systems, Keshav R. Acharya
Titchmarsh-Weyl Theory For Canonical Systems, Keshav R. Acharya
Publications
The main purpose of this paper is to develop Titchmarsh- Weyl theory of canonical systems. To this end, we first observe the fact that Schrodinger and Jacobi equations can be written into canonical systems. We then discuss the theory of Weyl m-function for canonical systems and establish the relation between the Weyl m-functions of Schrodinger equations and that of canonical systems which involve Schrodinger equations.
An Almost Periodic Function Of Several Variables With No Local Minimum, Gregory S. Spradlin
An Almost Periodic Function Of Several Variables With No Local Minimum, Gregory S. Spradlin
Publications
No abstract provided.