(b) By Parseval's formula ΣΙΑ*(v)||2 = ΣΣΚΑ*(vi), v;}/2 = ΣΣΚυ;, A(v;)}2 = ΣΙΑ(v;)||2 < 0. ji Request 2 + ΣΥΝΟΛΑ 2 Hence A* is a Hilbert-Schmidt operator.
(b) By Parseval's formula ΣΙΑ*(v)||2 = ΣΣΚΑ*(vi), v;}/2 = ΣΣΚυ;, A(v;)}2 = ΣΙΑ(v;)||2 < 0. ji Request 2 + ΣΥΝΟΛΑ 2 Hence A* is a Hilbert-Schmidt operator.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:28.2 Theorem
Let A E BL(H) be a Hilbert-Schmidt operator. Then
(a) A is compact.
(b) A* is a Hilbert-Schmidt operator.
(b) By Parseval's formula
Σ||A* (v₂) || ²2
i
=
ΣΣ|(A*(vi), vj)|²
ΣΣ(v₁, A(v;))|² = Σ|| A(v;)||² <∞.
ji
Hence A* is a Hilbert-Schmidt operator.
Request
explain
==11v11² 22
this dap
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