4 papers
Plancherel Identities for unbounded subsets of
Dorin Ervin Dutkay, Piyali Chakraborty
We present a class of pairs of subsets of for which the Fourier transform, when restricted to these subsets, is an isometric isomorphism, and thus the Plancherel iden…
Commuting self-adjoint extensions of the partial differential operators on disconnected sets
Piyali Chakraborty, Dorin Ervin Dutkay
In connection with the Fuglede conjecture, we study the existence of commuting self-adjoint extensions of the partial differential operators on arbitrary, possibly disconnected dom…
Some Plancherel identities for unbounded subsets of in duality
Piyali Chakraborty, Dorin Ervin Dutkay
In relation to Fuglede's conjecture, we establish several Plancherel-type identities and demonstrate the surjectivity of the Fourier transform between certain unbounded tiling sets…
Fuglede's conjecture, differential operators and unitary groups of local translations
Piyali Chakraborty, Dorin Ervin Dutkay, Palle E. T. Jorgensen
The purpose of the present paper is to address multiple aspects of the Fuglede question dealing (Fourier spectra vs geometry) with a variety of contexts where we make precise…