Fourier Multipliers for L2 Functions with Values in Nonseparable Hilbert Spaces and Operator-valued H Boundary Functions
نویسنده
چکیده
We extend the standard Fourier multiplier result to square integrable functions with values in (possibly nonseparable) Hilbert spaces. As a corollary, we extend the standard Hardy class boundary trace result to H (even Nevanlinna or bounded type) functions whose values are bounded linear operators between Hilbert spaces. Both results have been well-known in the case that the Hilbert spaces are separable. Naturally, the results apply to functions over the unit circle/disc or over the real-line/half-plane or over other similar domains, even multidimensional in the case of the multiplier result. We briefly treat some related results, generalizations to Banach spaces and counter-examples.
منابع مشابه
Operator-valued Fourier Multipliers in Besov Spaces and Its Applications
In recent years, Fourier multiplier theorems in vector–valued function spaces have found many applications in embedding theorems of abstract function spaces and in theory of differential operator equations, especially in maximal regularity of parabolic and elliptic differential–operator equations. Operator–valued multiplier theorems in Banach–valued function spaces have been discussed extensive...
متن کاملStochastic differential inclusions of semimonotone type in Hilbert spaces
In this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in F(t,x(t))dt +G(t,x(t))dW_t$ in which the multifunction $F$ is semimonotone and hemicontinuous and the operator-valued multifunction $G$ satisfies a Lipschitz condition. We define the It^{o} stochastic integral of operator set-valued stochastic pr...
متن کاملOperator-valued Bergman Inner Functions as Transfer Functions
An explicit construction characterizing the operator-valued Bergman inner functions is given for a class of vector-valued standard weighted Bergman spaces in the unit disk. These operator-valued Bergman inner functions act as contractive multipliers from the Hardy space into the associated Bergman space, and they have a natural interpretation as transfer functions for a related class of discret...
متن کاملCompact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions
We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.
متن کاملOperator-valued bases on Hilbert spaces
In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. We prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov-basis are continuous. We also dene the concepts of Bessel, Hilbert ov-basis and obta...
متن کامل