Advances in Inequalities of the Schwarz, Triangle and Heisenberg Type in Inner Product Spaces
The purpose of this book is to give a comprehensive introduction to several inequalities in Inner Product Spaces that have important applications in various topics of Contemporary Mathematics such as: Linear Operators Theory, Partial Differential Equations, Non-linear Analysis, Approximation Theory, Optimisation Theory, Numerical Analysis, Probability Theory, Statistics and other fields.
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2VmM a.e. t G Additive Reverses Applying Theorem assume Bessel's inequality best possible Bochner integrable Buzano clearly equivalent complex inner product complex number field complexification continuous triangle inequality deduce the desired defined desired inequality desired result elementary inequality equality holds follow the proof following corollary following inequality following refinement following result holds following reverse fora.e G a,b generalised triangle inequality Gram determinants Hadamard's inequality Heisenberg inequality hence hermitian form Hermitian functional Hilbert space holds true inequality in inner inner product space integral inequality IWI2 Kurepa Kurepa's Inequality Lebesgue integrable Lemma Let H obviously omit the details orthonormal family orthonormal vectors positive semi-definite Precupanu Proposition 48 prove the following real inner product real numbers real or complex Remark RGMIA Res S.S. Dragomir scalar Schwarz inequality space H superadditive Theorem Theorem 44 vectors in H