We introduce the B-spline interpolation problem corresponding to a C∗-valued sesquilinear form on Hilbert C∗-module and study its basic properties as well uniqueness of solution. first in case when is self-dual. Passing setting W∗-modules, we present our main result by characterizing spline for extended has Finally, solutions C∗-modules over C∗-ideals W∗-algebras are extensively discussed.

Let R be an associative ring with 1 and R the multiplicative group of invertible elements of R. In the paper, subgroups of R which may be regarded as analogues of the similitude group of a non-degenerate sesquilinear reflexive form and of the isometry group of such a form are defined in an abstract way. The main result states that a unipotent abstractly defined similitude must belong to the cor...

We apply functional analytical and variational methods in order to study well-posedness and qualitative properties of evolution equations on product Hilbert spaces. To this aim we introduce an algebraic formalism for matrices of sesquilinear mappings. We apply our results to parabolic problems of different nature: a coupled diffusive system arising in neurobiology, a strongly damped wave equati...

We consider linear inhomogeneous non-autonomous parabolic problems associated to sesquilinear forms, with discontinuous dependence of time. We show that for these problems, the property of maximal parabolic regularity can be extrapolated to time integrability exponents r 6= 2. This allows us to prove maximal parabolic L r-regularity for discontinuous non-autonomous second-order divergence form ...

Abstract A time–frequency transform is a sesquilinear mapping from suitable family of test functions to on the plane. The goal quantify energy present in signal at any given time and frequency. further specified by imposing conditions such as those stemming basic transformations signals which an density should satisfy. We systematic study how properties are reflected associated evaluation origi...

In this paper we present a signal reconstruction algorithm from absolute value of frame coefficients that requires a relatively low redundancy. The basic idea is to use a nonlinear embedding of the input signal Hilbert space into a higher dimensional Hilbert space of sesquilinear functionals so that absolute values of frame coefficients are associated to relevant inner products in that space. I...

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