世俗
发表于 2025-3-23 10:29:47
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.
残忍
发表于 2025-3-23 15:44:18
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 ..
先驱
发表于 2025-3-23 20:19:42
Convexity, IV: Bhatia–Hiai–Sano (BHS) TheoremIn Chapter ., given a .. function, ., on ., we defined the Loewner matrix by.
思想上升
发表于 2025-3-24 01:07:05
Convexity, V: Strongly Operator Convex FunctionsLet . be a real-valued function on ..
nostrum
发表于 2025-3-24 03:36:07
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
发表于 2025-3-24 06:33:48
Quadratic Interpolation: The Foiaş–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
发表于 2025-3-24 11:40:28
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曲解
发表于 2025-3-24 18:14:36
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
发表于 2025-3-24 20:10:15
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清楚说话
发表于 2025-3-25 02:10:46
978-3-030-22424-0Springer Nature Switzerland AG 2019