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Let $$f:[0,\infty )\rightarrow [0,\infty )$$f:[0,∞)→[0,∞) be an operator monotone function and $$g: \mathbb {R}\rightarrow [0,\infty )$$g:R→[0,∞) be a conditionally negative definite(in short cnd) function. We obtain that $$f\circ g:\mathbb {R}\rightarrow… Click to show full abstract
Let $$f:[0,\infty )\rightarrow [0,\infty )$$f:[0,∞)→[0,∞) be an operator monotone function and $$g: \mathbb {R}\rightarrow [0,\infty )$$g:R→[0,∞) be a conditionally negative definite(in short cnd) function. We obtain that $$f\circ g:\mathbb {R}\rightarrow [0,\infty )$$f∘g:R→[0,∞) is also conditionally negative definite. This generalizes and subsumes several existing results. A versatile direct connection between cnd functions and functions having Weierstrass factorization is established and consequently a reasonable account for cnd functions is presented.
Journal Title: Mediterranean Journal of Mathematics
Year Published: 2018
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