Eigenfunction expansions and the pinsky phenomenon on compact manifolds

2001 ◽  
Vol 7 (5) ◽  
pp. 507-522 ◽  
Author(s):  
Michael Taylor
Keyword(s):  
Compact Manifolds ◽  
Eigenfunction Expansions ◽  
Pinsky Phenomenon

scholarly journals Eigenfunction Expansions of Ultradifferentiable Functions and Ultradistributions. III. Hilbert Spaces and Universality

2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Aparajita Dasgupta ◽  
Michael Ruzhansky
Keyword(s):  
Hilbert Spaces ◽  
Sequence Spaces ◽  
Compact Manifolds ◽  
Tensor Structure ◽  
Eigenfunction Expansions ◽  
Ultradifferentiable Functions ◽  
Perfect Sequence ◽  
In Trans

AbstractIn this paper we analyse the structure of the spaces of smooth type functions, generated by elements of arbitrary Hilbert spaces, as a continuation of the research in our papers (Dasgupta and Ruzhansky in Trans Am Math Soc 368(12):8481–8498, 2016) and (Dasgupta and Ruzhansky in Trans Am Math Soc Ser B 5:81–101, 2018). We prove that these spaces are perfect sequence spaces. As a consequence we describe the tensor structure of sequential mappings on the spaces of smooth type functions and characterise their adjoint mappings. As an application we prove the universality of the spaces of smooth type functions on compact manifolds without boundary.

scholarly journals Theorems of Chernoff and Ingham for certain eigenfunction expansions

2021 ◽  
Vol 386 ◽  
pp. 107815
Author(s):  
Pritam Ganguly ◽  
Sundaram Thangavelu
Keyword(s):  
Eigenfunction Expansions
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