000			a
999			_c32365 _d32365
008			230829b xxu||||| |||| 00| 0 eng d
020			_a9783658204563
082			_a515.723 _bVOL
100			_aVolland, Dominik
245			_aDiscrete Hilbert transform with circle packings
260			_bSpringer Spektrum, _c2017 _aWiesbaden :
300			_axi, 102 p. ; _bill., (some color), _c21 cm
365			_b49.99 _cEUR _d94.90
490			_aBest Masters
504			_aIncludes bibliographical references.
520			_aDominik Volland studies the construction of a discrete counterpart to the Hilbert transform in the realm of a nonlinear discrete complex analysis given by circle packings. The Hilbert transform is closely related to Riemann-Hilbert problems which have been studied in the framework of circle packings by E. Wegert and co-workers since 2009. The author demonstrates that the discrete Hilbert transform is well-defined in this framework by proving a conjecture on discrete problems formulated by Wegert. Moreover, he illustrates its properties by carefully chosen numerical examples. Basic knowledge of complex analysis and functional analysis is recommended. Contents Hardy Spaces and Riemann-Hilbert Problems The Hilbert Transform in the Classical Setting Circle Packings Discrete Boundary Value Problems Discrete Hilbert Transform Numerical Results of Test Computations Properties of the Discrete Transform Target Groups Lecturers and students of mathematics who are interested in circle packings and/or discrete Riemann-Hilbert problems.
650			_aBanach space
650			_a Boundary value problem
650			_aCircle packing
650			_a Harmonic functions
650			_aHolomorphic functions
650			_aHRHP
650			_aMaximal packing
650			_aRiemann-Hilbert problem
942			_2ddc _cBK