- Recursively defined functions and their zero distribution

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Polynomials related to orthogonal functions or arising from number theory often satisfy a three term-recurrence. We set out to establish the asymptotic zero distribution of (matrix) polynomials satisfying such recurrence via elementary methods. We try to avoid arguments based on 'normal families' of function families or 'finite sections' of infinite Toeplitz operators. Instead we use standard fix point arguments of analysis, and continued fraction results of number-theory. First proof of concept is the first full discussion of Fibonacci polynomials.

Extension to recursions generated by rational functions are investigated.

Extension to recursions generated by rational functions are investigated.