INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS
Scope & Guideline
Transforming Ideas into Mathematical Insights
Introduction
Aims and Scopes
- Integral Transforms:
The journal emphasizes the study and development of various integral transforms including Fourier, Laplace, Mellin, and their generalized forms. This includes explorations of their properties, applications, and innovations in their computational techniques. - Special Functions:
A significant focus is placed on special functions such as Bessel, Laguerre, and orthogonal polynomials, exploring their properties, interrelations, and applications in solving differential equations and other mathematical problems. - Functional Analysis:
The journal encompasses research on functional analytic methods, including the study of function spaces, operator theory, and the application of integral transforms in functional analysis. - Pseudo-differential Operators:
Research related to pseudo-differential operators and their applications in various areas of mathematics, particularly in relation to integral transforms, is a consistent theme within the journal. - Applications in Physics and Engineering:
Many articles explore the applications of integral transforms and special functions in physics and engineering, particularly in areas such as signal processing, quantum mechanics, and mathematical physics. - Theoretical Mathematics:
The journal also publishes theoretical research that advances the understanding of integral transforms and special functions, contributing to the broader field of mathematics.
Trending and Emerging
- Fractional Calculus and Transforms:
There is an increasing focus on fractional calculus and its applications, particularly in the context of fractional Fourier transforms and fractional differential equations, highlighting a growing interest in non-integer order derivatives. - Wavelet Transforms and Time-Frequency Analysis:
Wavelet transforms and their applications in time-frequency analysis are becoming more prominent, indicating a trend towards exploring how these methods can provide insights into signal processing and data analysis. - Computational Techniques and Algorithms:
Emerging themes include the development of new computational techniques and algorithms for evaluating integral transforms and special functions, reflecting the need for efficient methods in both theoretical and applied mathematics. - Multi-dimensional and Generalized Transforms:
Research on multi-dimensional and generalized transforms is trending, showcasing an interest in expanding the traditional frameworks of integral transforms to accommodate more complex scenarios. - Interdisciplinary Applications:
There is a noticeable increase in the exploration of interdisciplinary applications, particularly in physics, engineering, and computer science, indicating a trend where mathematical innovations are being utilized in practical contexts.
Declining or Waning
- Classical Orthogonal Polynomials:
Although classical orthogonal polynomials have been a staple of the journal, there seems to be a waning interest in purely classical approaches, with fewer publications focusing solely on these topics without a modern context. - Basic Integral Representations:
Research centered around basic integral representations of functions has seen a decline, possibly due to the increasing complexity and specialization of topics in recent publications. - Elementary Functions:
There is a noticeable decrease in publications that focus on elementary functions and their basic properties, as the journal leans more towards advanced mathematical concepts and applications.
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