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Results tagged with ca.classical-analysis-and-odes
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user 490101
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
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Construction of the Lipschitz function with a given Lipschitz constant and given two values
Let the function $f\colon [a,b] \to\mathbb{C}$ be Lipschitz and let $|f(a)| \geq c$ and $|f(b)| = c$. Is there a Lipschitz function $g$ such that $|g| \geq c,$ $g(a)=f(a),$ $ g(b)=f(b)$ and Lipschitz …
- 97
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Construction of the Lipschitz function with a given Lipschitz constant, given two values and...
Let the function $f\colon [a,b] \to\mathbb{C}$ be Lipschitz and let $|f(a)| \geq c,$ $|f(b)| = c$ and $\varepsilon > 0.$
It is easy to see that if $\|f\|_{\infty}< \frac{\varepsilon}{2} =: \delta (\va …
- 97