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Inequalities from Complex Analysis
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    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Dostert, Maria Guzmán, Cristóbal Filho, Fernando Mário de Oliveira and Vallentin, Frank 2017. New Upper Bounds for the Density of Translative Packings of Three-Dimensional Convex Bodies with Tetrahedral Symmetry. Discrete & Computational Geometry,

    D’Angelo, John P. 2016. Complex Variables Throughout the Curriculum. PRIMUS, p. 1.

    Bolt, Michael and Raich, Andrew 2015. The Kerzman–Stein operator for piecewise continuously differentiable regions. Complex Variables and Elliptic Equations, Vol. 60, Issue. , p. 478.

    Knese, Greg 2015. Integrability and regularity of rational functions:. Proceedings of the London Mathematical Society, Vol. 111, Issue. , p. 1261.

    D'ANGELO, JOHN P. and PUTINAR, MIHAI 2012. HERMITIAN COMPLEXITY OF REAL POLYNOMIAL IDEALS. International Journal of Mathematics, Vol. 23, Issue. , p. 1250026.

    D’Angelo, John P. and Lebl, Jiří 2011. Hermitian Symmetric Polynomials and CR Complexity. Journal of Geometric Analysis, Vol. 21, Issue. , p. 599.

    Raich, Andrew 2010. Compactness of the complex Green operator on CR-manifolds of hypersurface type. Mathematische Annalen, Vol. 348, Issue. , p. 81.

    Adali, Tülay and Li, Hualiang 2010. Adaptive Signal Processing. p. 1.

    Buescu, Jorge and Paixão, A.C. 2006. A linear algebraic approach to holomorphic reproducing kernels in <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="" xmlns:xs="" xmlns:xsi="" xmlns="" xmlns:ja="" xmlns:mml="" xmlns:tb="" xmlns:sb="" xmlns:ce="" xmlns:xlink="" xmlns:cals=""><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">C</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>. Linear Algebra and its Applications, Vol. 412, Issue. , p. 270.

    D'ANGELO, JOHN P. 2005. COMPLEX VARIABLES ANALOGUES OF HILBERT'S SEVENTEENTH PROBLEM. International Journal of Mathematics, Vol. 16, Issue. , p. 609.

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    Inequalities from Complex Analysis
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Book description

Inequalities from Complex Analysis is a careful, friendly exposition of inequalities and positivity conditions for various mathematical objects arising in complex analysis. The author begins by defining the complex number field, and then discusses enough mathematical analysis to reach recently published research on positivity conditions for functions of several complex variables. The development culminates in complete proofs of a stabilization theorem relating two natural positivity conditions for real-valued polynomials of several complex variables. The reader will also encounter the Bergman kernel function, Fourier series, Hermitian linear algebra, the spectral theorem for compact Hermitian operators, plurisubharmonic functions, and some delightful inequalities. Numerous examples, exercises, and discussions of geometric reasoning appear along the way. Undergraduate mathematics majors who have seen elementary real analysis can easily read the first five chapters of this book, and second year graduate students in mathematics can read the entire text. Some physicists and engineers may also find the topics and discussions useful. The inequalities and positivity conditions herein form the foundation for a small but beautiful part of complex analysis. John P. D'Angelo was the 1999 winner of the Bergman Prize; he was cited for several important contributions to complex analysis, including his work on degenerate Levi forms and points of finite type, as well as work, some joint with David Catlin, on positivity conditions in complex analysis


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