Functional Analysis, Function Norms and Control Signals

  • Alexander Weinmann


Consider a function f with the value f(t) at a certain instant t and assume that the integral of the pth power of the absolute value |f(t)| exists within a region R. Then, this function f is said to be within the function space (or set of functions) Lp(R). In most cases, R is given by an interval [to, ∞). The function norm ∥If∥p of the entire function f is defined by
$${\left\| f \right\|_p} \buildrel \Delta \over = {\left[ {\int_R {{{\left| {f(t)} \right|}^p}} dt} \right]^{1/p}}{\rm{ }}\forall p \in \left[ {1,\infty )} \right.$$


Function Space Hardy Space Linear Quadratic Regulator Holder Inequality Infinity Norm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Wien 1991

Authors and Affiliations

  • Alexander Weinmann
    • 1
  1. 1.Department of Electrical EngineeringTechnical University ViennaAustria

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