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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.

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Prove that $f(0+)=f(0)$ if $f \in R(\beta_1)$ [closed]

Let $\beta_1$ be a function defined by $$\beta_1(x)= \begin{cases} 0 & x \le 0\\ 1 & x >0 \end{cases} $$ Now we define $f(x)$ which is a bounded function on $[-1,1]$. We need to how that $ f \in R(\b …