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square-integrable function

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1: 1.4 Calculus of One Variable
Square-Integrable Functions
A function f ( x ) is square-integrable if …
2: 28.30 Expansions in Series of Eigenfunctions
Then every continuous 2 π -periodic function f ( x ) whose second derivative is square-integrable over the interval [ 0 , 2 π ] can be expanded in a uniformly and absolutely convergent series …
3: 30.4 Functions of the First Kind
If f ( x ) is mean-square integrable on [ - 1 , 1 ] , then formally …
4: 33.22 Particle Scattering and Atomic and Molecular Spectra
§33.22(i) Schrödinger Equation
§33.22(iv) Klein–Gordon and Dirac Equations
  • Eigenstates using complex-rotated coordinates r r e i θ , so that resonances have square-integrable eigenfunctions. See for example Halley et al. (1993).

  • 5: 1.8 Fourier Series
    Let f ( x ) be an absolutely integrable function of period 2 π , and continuous except at a finite number of points in any bounded interval. …
    §1.8(iii) Integration and Differentiation
    when f ( x ) and g ( x ) are square-integrable and a n , b n and a n , b n are their respective Fourier coefficients. … Suppose that f ( x ) is twice continuously differentiable and f ( x ) and | f ′′ ( x ) | are integrable over ( - , ) . … Suppose also that f ( x ) is integrable on [ 0 , ) and f ( x ) 0 as x . …