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Calculus On Linear Recurrence Sequences
Spectral and Jordan Operators on Linear Recurrences
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About the Book
What if every linear recurrence sequence carried its own calculus?
Calculus on Linear Recurrence Sequences develops a new operator-theoretic framework in which recurrence sequences generate spectral operators, generalized derivatives, and entire families of calculi. Starting from characteristic roots and Binet representations, the book builds a theory connecting recurrence sequences, operator theory, spectral geometry, and generalized differentiation.
The current edition introduces the foundations of the theory: linear recurrences, Binet representations, the spectral Binet operator, the U-derivative, iteration theory, spectral product rules, Leibniz defects, quotient rules, and the first steps toward a classification of recurrence-induced calculi.
This is a living research monograph written alongside an active mathematical research program. New chapters are added regularly as the theory evolves.
Planned Future Topics
Ward Calculus
Bilateral and Non-Ward Calculus
Singular Recurrence Calculi
Spectral-Jordan Operators
Recurrence Integration
Operator Equivalence and Classification
Functional Equations and Special Functions
Open Problems and Research Directions
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