Transactions in Theoretical and Mathematical Physics

Transactions in Theoretical and Mathematical Physics

Equivalent classes of square – integrable functions in the Hilbert space

Document Type : Original Article

Author
Mehdi Jafari Matehkolaee
Department of Physics, Amirkabir University of Technology (Tehran Polytechnic ), P.O.Box: 15875-4413,Tehran, Iran
10.30511/ttmp.2025.2054761.1050
Abstract
In this paper we have discussed that the members of the Hilbert space are indeed not square-integrable functions themselves, but rather the members are equivalent classes of these functions. Contemplating on these functions compels us to make a distinction between two operators. First, the ordinary derivative , is just the usual partial differentiation which acts on the scalar function; and should not be considered as an operator which can act on the vectors in the Hilbert space. Second, unbounded operator , which is usually mixed up with the former.
Keywords
square-integrable function
ordinary derivative
differential operator
Subjects
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Transactions in Theoretical and Mathematical Physics
Volume 2, Issue 2
Spring 2025
Pages 66-69

  • Receive Date 01 March 2025
  • Revise Date 04 May 2025
  • Accept Date 17 May 2025
  • First Publish Date 17 May 2025
  • Publish Date 01 May 2025