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The inverse function theorem and the Jacobian conjecture for free analysis

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Abstract

We establish an invertibility criterion for free polynomials and free functions evaluated on some tuples of matrices. We show that if the derivative is nonsingular on some domain closed with respect to direct sums and similarity, the function must be invertible. Thus, as a corollary, we establish the Jacobian conjecture in this context. Furthermore, our result holds for commutative polynomials evaluated on tuples of commuting matrices.

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  1. Department of Mathematics, University of California, San Diego, 9500 Gilman Drive # 0112, La Jolla, CA, 92093-0112, USA

    J. E. Pascoe

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  1. J. E. Pascoe
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Pascoe, J.E. The inverse function theorem and the Jacobian conjecture for free analysis. Math. Z. 278, 987–994 (2014). https://doi.org/10.1007/s00209-014-1342-2

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  • DOI: https://doi.org/10.1007/s00209-014-1342-2

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