Abstract:We consider the problem of minimizing the distance f − φ L p (K ) , where K is a subset of the complex unit circle ∂D and φ ∈ C(K ), subject to the constraint that f lies in the Hardy space H p (D) and | f | ≤ g for some positive function g. This problem occurs in the context of filter design for causal LTI systems. We show that the optimization problem has a unique solution, which satisfies an extremal property similar to that for the Nehari problem. Moreover, we prove that the minimum of the optimization pro… Show more
we consider the extremal problem of best approximation to some function f in L 2 (I), with I a subset of the circle, by the trace of a Hardy function whose modulus is bounded pointwise by some gauge function on the complementary subset.
we consider the extremal problem of best approximation to some function f in L 2 (I), with I a subset of the circle, by the trace of a Hardy function whose modulus is bounded pointwise by some gauge function on the complementary subset.
we consider the extremal problem of best approximation to some function f in L 2 (I), with I a subset of the circle, by the trace of a Hardy function whose modulus is bounded pointwise by some gauge function on the complementary subset.
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