Linear Differential Equations in Banach Spaces
Linear Differential Equations in Banach Spaces
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In our eReader you can find the full English version of the book. Read Linear Differential Equations in Banach Spaces Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Linear Differential Equations in Banach Spaces
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3) to (2. 6) can be established without relying on Phillips' results. We need only put * Actually the condition given by Phillips is more general than (2. 7) in that the right-hand side of his equation contains (x-co)" instead of x" • The difference is not essential, hovfevsr, since either form can be reduced to the other by using A + col instead of A. We have chosen the form (2. 7) for convenience of comparison with the case (2. 2).
- 5 - (2. 8) exp(tA) - Q"-"- exp(tl) Q, where exp(tA) is defi...ned by Hille-Yosida theorem. Note also that since (XI-a)~ ■ Q~ (XI-A)" Q, all positive real numbers belong to the resolvent set of A.
3. Uniqueness theorem After these preliminaries we retvirn to the general case with time -dependent A(t) and introduce the following assumption.
Assumption 1 . For each t, a so that there is a bounded linear operator Q(t) with a bounded inverse Q(t)" such that A(t) » Q(t)A(t)Q(t)'' & (S). Moreover Q(t) is strongly continuously differentiable, that is, the strong derivative Q(t) « dQ(t)/dt exists and is strongly continuous.
What to read after Linear Differential Equations in Banach Spaces?
You can find similar books in the "Read Also" column, or choose other free books by Tosio Kato to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
3) to (2. 6) can be established without relying on Phillips' results. We need only put * Actually the condition given by Phillips is more general than (2. 7) in that the right-hand side of his equation contains (x-co)" instead of x" • The difference is not essential, hovfevsr, since either form can be reduced to the other by using A + col instead of A. We have chosen the form (2. 7) for convenience of comparison with the case (2. 2).
- 5 - (2. 8) exp(tA) - Q"-"- exp(tl) Q, where exp(tA) is defi...ned by Hille-Yosida theorem. Note also that since (XI-a)~ ■ Q~ (XI-A)" Q, all positive real numbers belong to the resolvent set of A.
3. Uniqueness theorem After these preliminaries we retvirn to the general case with time -dependent A(t) and introduce the following assumption.
Assumption 1 . For each t, a so that there is a bounded linear operator Q(t) with a bounded inverse Q(t)" such that A(t) » Q(t)A(t)Q(t)'' & (S). Moreover Q(t) is strongly continuously differentiable, that is, the strong derivative Q(t) « dQ(t)/dt exists and is strongly continuous.
What to read after Linear Differential Equations in Banach Spaces?
You can find similar books in the "Read Also" column, or choose other free books by Tosio Kato to read onlineMoreLess
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