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Spectral Shift Function and Eigenvalues of the Perturbed Operator
In the space of square integrable functions on the positive semi-axis, two positive self-adjoint operators generated by a one-dimensional free...
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A note on the cosine operator function for Mellin sampling series
The theory of sampling operators is one of the major areas of analysis in which Paul Leo Butzer and his colleagues/students have achieved long-term...
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The Livšic function of a homogeneous symmetric operator and the multiplication theorem
This paper presents a solution to the Jørgensen–Muhly problem for a homogeneous symmetric operator with deficiency indices (1, 1) that does not admit ...
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The Associated Operator Legendre Function and the Incomplete Cauchy Problem
AbstractUsing the concept of a fractional integral of a function with respect another function, a new operator function, called the associated...
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When is an operator S an analytic function of an operator T ?
We give necessary and sufficient conditions for an operator S on a Banach space to be an analytic function of a non-algebraic operator T . We extend...
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A new weighted fractional operator with respect to another function via a new modified generalized Mittag–Leffler law
In this paper, new generalized weighted fractional derivatives with respect to another function are derived in the sense of Caputo and...
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A closure operator respecting the modular j-function
We prove some unconditional cases of the Existential Closedness problem for the modular j -function. For this, we show that for any finitely generated...
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Approximation of the Lebesgue Constant of the Fourier Operator by a Logarithmic-Fractional-Rational Function
AbstractThe Lebesgue constant of the classical Fourier operator is uniformly approximated by a logarithmic-fractional-rational function depending on...
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On Common Borel Direction of Entire Function f and Its q-Difference Operator
The common Borel direction of entire function f ( z ) and its q -difference operator is studied by using Nevanlinna theory. Some conditions of the...
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On Generalized Shannon Sampling Operators in the Cosine Operator Function Framework
The aim of this work is to study generalized Shannon sampling operators, where the kernel function is defined via the Fourier transform of a certain...
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Asymptotic analysis of three-parameter Mittag-Leffler function with large parameters, and application to sub-diffusion equation involving Bessel operator
In this paper, we apply the steepest descent method to the Schläfli-type integral representation of the three-parameter Mittag-Leffler function...
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Convexity Estimates for Green’s Function and the First Eigenfunction of Laplace Operator
In this paper, we find some superharmonic functions, which relate to the convexity estimates for Green’s function and the first eigenfunction of...
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Fractional Operator Associated with the Fractal Integral of A-Fractal Function
An advanced calculus called the fractal calculus is formulated as a generalization of ordinary calculus and it is being applied to functions with...
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On the uniqueness of a meromorphic function and its higher difference operator under the purview of two shared sets
In the paper, we investigate the uniqueness problem of a meromorphic function and its difference operator to the most general setting via two shared...
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Application of the Green–Samoilenko Function and Operator to the Investigation of Non-Lipschitz Differential Equations
For systems of non-Lipschitz differential equations, we establish conditions for the existence of invariant sets. To obtain this result, we apply the...