On an inversion formula
نویسندگان
چکیده
منابع مشابه
Inversion Formula for Continuous Multifractals
In a previous paper MR the authors introduced the inverse measure y of a probability measure on It was argued that the respective multifractal spectra are linked by the inversion formula fy f Here the statements of MR are put in more mathematical terms and proofs are given for the inversion formula in the case of continuous measures Thereby f may stand for the Hausdor spectrum the packing spect...
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In this article we present an improved exact inversion formula for the 3D cone beam transform of vector fields. It is well known that only the solenoidal part of a vector field can be determined by the longitudinal ray transform of a vector field in cone beam geometry. The exact inversion formula, as it was developed in A. Katsevich and T. Schuster, An exact inversion formula for cone beam vect...
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Wilf stated that the Lagrange inversion formula (LIF) is a remarkable tool for solving certain kinds of functional equations, and at its best it can give explicit formulas where other approaches run into stone walls. Here we present the LIF combinatorially in the form of lattice paths, and apply it to the divisibility property of the coefficients of a formal power series expansion. For the LIF,...
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Examples. Let n ∈ N. Define functions τ, σ, π : N → N as follows: • τ(n) = the number of all natural divisors of n = #{d > 0 | d|n}; • σ(n) = the sum of all natural divisors of n = ∑ d|nd; • π(n) = the product of all natural divisors of n = ∏ d|nd. As we shall see below, τ and σ are multiplicative functions, while π is not. From now on we shall write the prime decomposition of n ∈ N as n = p1 1...
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 1983
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s001708950000522x