scholarly journals Reachable states and holomorphic function spaces for the 1-D heat equation

2020 ◽  
pp. 108852
Author(s):  
Marcu-Antone Orsoni
Keyword(s):  
Holomorphic Function ◽  
Heat Equation ◽  
Function Spaces

Reverse Hypercontractivity for Subharmonic Functions

2005 ◽  
Vol 57 (3) ◽  
pp. 506-534 ◽  
Author(s):  
Leonard Gross ◽  
Martin Grothaus
Keyword(s):  
Holomorphic Function ◽  
Dirichlet Form ◽  
Function Spaces ◽  
Subharmonic Functions ◽  
Lower Boundedness

AbstractContractivity and hypercontractivity properties of semigroups are now well understood when the generator, A, is a Dirichlet form operator. It has been shown that in some holomorphic function spaces the semigroup operators, e−tA, can be bounded below from Lp to Lq when p, q and t are suitably related. We will show that such lower boundedness occurs also in spaces of subharmonic functions.

scholarly journals Isometric and Closed-Range Composition Operators between Bloch-Type Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-15
Author(s):  
Nina Zorboska
Keyword(s):  
Holomorphic Function ◽  
Composition Operators ◽  
Function Spaces ◽  
Complete Characterization ◽  
Closed Range ◽  
Different Types ◽  
Type Spaces ◽  
Range Determination

We present an overview of the known results describing the isometric and closed-range composition operators on different types of holomorphic function spaces. We add new results and give a complete characterization of the isometric univalently induced composition operators acting between Bloch-type spaces. We also add few results on the closed-range determination of composition operators on Bloch-type spaces and present the problems that are still open.

scholarly journals An improved characterisation of regular generalised functions of white noise and an application to singular SPDEs

2021 ◽  
Author(s):  
Martin Grothaus ◽  
Jan Müller ◽  
Andreas Nonnenmacher
Keyword(s):  
Holomorphic Function ◽  
Heat Equation ◽  
Multiplicative Noise ◽  
Complex Numbers ◽  
One Dimensional ◽  
Infinite Dimensional ◽  
Stochastic Transport ◽  
The One ◽  
Funct Anal ◽  
Stochastic Transport Equation

AbstractA characterisation of the spaces $${\mathcal {G}}_K$$ G K and $${\mathcal {G}}_K'$$ G K ′ introduced in Grothaus et al. (Methods Funct Anal Topol 3(2):46–64, 1997) and Potthoff and Timpel (Potential Anal 4(6):637–654, 1995) is given. A first characterisation of these spaces provided in Grothaus et al. (Methods Funct Anal Topol 3(2):46–64, 1997) uses the concepts of holomorphy on infinite dimensional spaces. We, instead, give a characterisation in terms of U-functionals, i.e., classic holomorphic function on the one dimensional field of complex numbers. We apply our new characterisation to derive new results concerning a stochastic transport equation and the stochastic heat equation with multiplicative noise.

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