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- Canonical systems (2)
- De Branges theorem (1)
- Financial mathematics (1)
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- Integrating factor (1)
- Isospectral potentials (1)
- Least gradient problem (1)
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- Riccati equation (1)
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- Traces of functions of bounded variation (1)
- Weyl-m functions (1)
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Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
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.
One-Parameter Families Of Supersymmetric Isospectral Potentials From Riccati Solutions In Function Composition Form, Haret C. Rosu, S.C. Mancas, Pisin Chen
One-Parameter Families Of Supersymmetric Isospectral Potentials From Riccati Solutions In Function Composition Form, Haret C. Rosu, S.C. Mancas, Pisin Chen
Publications
In the context of supersymmetric quantum mechanics, we define a potential through a particular Riccati solution of the composition form (F∘f)(x)=F(f(x)) and obtain a generalized Mielnik construction of one-parameter isospectral potentials when we use the general Riccati solution. Some examples for special cases of F and f are given to illustrate the method. An interesting result is obtained in the case of a parametric double well potential generated by this method, for which it is shown that the parameter of the potential controls the heights of the localization probability in the two wells, and for certain values of the parameter …
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.
Not All Traces On The Circle Come From Functions Of Least Gradient In The Disk, Gregory S. Spradlin, Alexandru Tamasan
Not All Traces On The Circle Come From Functions Of Least Gradient In The Disk, Gregory S. Spradlin, Alexandru Tamasan
Publications
We provide an example of an L¹ function on the circle, which cannot be the trace of a function of bounded variation of least gradient in the disk.
A Regression Model To Investigate The Performance Of Black-Scholes Using Macroeconomic Predictors, Timothy A. Smith, Ersoy Subasi, Aliraza M. Rattansi
A Regression Model To Investigate The Performance Of Black-Scholes Using Macroeconomic Predictors, Timothy A. Smith, Ersoy Subasi, Aliraza M. Rattansi
Publications
As it is well known an option is defined as the right to buy sell a certain asset, thus, one can look at the purchase of an option as a bet on the financial instrument under consideration. Now while the evaluation of options is a completely different mathematical topic than the prediction of future stock prices, there is some relationship between the two. It is worthy to note that henceforth we will only consider options that have a given fixed expiration time T, i.e., we restrict the discussion to the so called European options. Now, for a simple illustration of …
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.