4 citations · 7 across the 9 of their papers we have counts for
9 papers
Projection-based approximations for eigenvalue problems of Fredholm integral operators with Green's kernels
Shashank K. Shukla, Gobinda Rakshit, Akshay S. Rane
We consider the eigenvalue problem . Our analysis focuses on the convergence rates of eigenvalue and spectral subspace approximations for compact linear integral operator…
Asymptotic expansions for approximate solutions of boundary integral equations
Akshay Rane, Kunalkumar Shelar
This paper uses the Modified Projection Method to examine the errors in solving the boundary integral equation from Laplace equation. The analysis uses weighted norms, and parallel…
Joint spectrum of matrix and operator tuples on spaces over bi complex numbers
Akshay Rane
In this paper, we generalize the notion of joint eigenvalues and joint spectrum of matrices and operator tupples on a bi complex Hilbert space. We observe that unlike the spectrum…
A note on improvement by iteration for the approximate solutions of second kind Fredholm integral equations with Green's kernels
Gobinda Rakshit, Shashank K. Shukla, Akshay S. Rane
Consider a linear operator equation , where is given and is a Fredholm integral operator with a Green's function type kernel defined on . For $r \geq 0…
Spectral Theorem for a bounded self adjoint operator on a Bicomplex Hilbert space
Akshay Sakharam Rane
In this paper, we shall consider the notion of bicomplex inner product and define bicomplex Hilbert space. We shall define where the functions take bicomplex values. W…
Zabreiko's Lemma with Bicomplex and hyperbolic scalars and its applications
Akshay S. Rane, Mandar Thatte
In this paper, we shall consider the notion of hyperbolic semi norm which on a module to set of all positive hyperbolic numbers. We shall prove the characterization of continui…
Zabreiko's lemma in 2-normed space and its applications
Akshay S. Rane
We prove the Zabreiko's lemma in 2-Banach spaces. As an application we shall prove a version of the closed graph theorem and open mapping theorem.
A note on the 2-dual space of
Akshay S. Rane
In the present note, we are interested in bounded 2-functionals and 2-dual spaces of . The 2-dual spaces of the sequence space is considered in the literature. But…
Richardson extrapolation for the iterated Galerkin solution of Urysohn integral equations with Green's kernels
Gobinda Rakshit, Akshay S. Rane, Kshitij Patil
We consider a Urysohn integral operator with kernel of the type of Green's function. For , a space of piecewise polynomials of degree with respe…