Titlebook: Loewner‘s Theorem on Monotone Matrix Functions; Barry Simon Book 2019 Springer Nature Switzerland AG 2019 matrix convex.approximation theo

世俗

Convexity, II: Concavity and MonotonicityThis chapter will first provide a remarkable equivalence between matrix concavity and matrix monotonicity for positive functions not even hinted at in the scalar case. Then we’ll discuss a connection between matrix convexity and Loewner matrices.

殘忍

Convexity, III: Hansen–Jensen–Pedersen (HJP) InequalityJensen’s inequality in its original form says that if . is a scalar convex function (on an open convex set, ., of a vector space, V) and if . with ., then ..

先驅(qū)

Convexity, IV: Bhatia–Hiai–Sano (BHS) TheoremIn Chapter ., given a .. function, ., on ., we defined the Loewner matrix by.

思想上升

Convexity, V: Strongly Operator Convex FunctionsLet . be a real-valued function on ..

nostrum

2?×?2 Matrices: The Donoghue and Hansen–Tomiyama TheoremsLoewner’s theorem provides a simple characterization of . but it is not so simple to describe which functions are in a general ..

鬼魂

Quadratic Interpolation: The Foia?–Lions TheoremIn this chapter, we’ll begin by considering a mathematically interesting problem that seems unconnected to the subject of matrix monotone functions.

Traumatic-Grief

曲解

Pick Interpolation, II: Hilbert Space ProofOur goal here is to prove the following part of Theorem . which, by the results of the last chapter, completes the proofs of Theorems ., ., and ..

硬化

清楚說話

978-3-030-22424-0Springer Nature Switzerland AG 2019