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.
Jafari Matehkolaee,M. (2025). Equivalent classes of square – integrable functions in the Hilbert space. Transactions in Theoretical and Mathematical Physics, 2(2), 66-69. doi: 10.30511/ttmp.2025.2054761.1050
MLA
Jafari Matehkolaee,M. . "Equivalent classes of square – integrable functions in the Hilbert space", Transactions in Theoretical and Mathematical Physics, 2, 2, 2025, 66-69. doi: 10.30511/ttmp.2025.2054761.1050
HARVARD
Jafari Matehkolaee M. (2025). 'Equivalent classes of square – integrable functions in the Hilbert space', Transactions in Theoretical and Mathematical Physics, 2(2), pp. 66-69. doi: 10.30511/ttmp.2025.2054761.1050
CHICAGO
M. Jafari Matehkolaee, "Equivalent classes of square – integrable functions in the Hilbert space," Transactions in Theoretical and Mathematical Physics, 2 2 (2025): 66-69, doi: 10.30511/ttmp.2025.2054761.1050
VANCOUVER
Jafari Matehkolaee M. Equivalent classes of square – integrable functions in the Hilbert space. TTMP, 2025; 2(2): 66-69. doi: 10.30511/ttmp.2025.2054761.1050
