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Unitary dilations of contraction operators

100%

Mlak W.

Instytut Matematyczny Polskiej Akademii Nauk

EN

Contents Preliminaries.................................................................................... 3 1. Notation and definitions............................................................. 6 2. Simple unitary dilations............................................................. 8 3. Dilation theorem.......................................................................... 12 4. Unitary dilation of a single contractions.................................. 22 5. Decomposition theorems......................................................... 30 6. Bilateral shifts.............................................................................. 36 7. Some spectral relations............................................................ 46 8. Properties of spectral-harmonic measures.......................... 50 9. Functional calculus..................................................................... 61 10. One-parameter semi-groups of contractions..................... 71 11. Sz.-Nagy-Brehmer dilations.................................................... 78 References....................................................................................... 86 Index of terms................................................................................... 89 Index of symbols.............................................................................. 90

2

An example of the equation $u_t = u_{xx} + f(x, t, u)$ with distinct maximum and minimum solutions of a mixed problem

59%

Mlak W.

Annales Polonici Mathematici

|

1963

|

tom 13

|

nr 1

101-103

3

Estimates of solutions of hyperbolic systems of differential equations in two independent variables

59%

Mlak W.

Annales Polonici Mathematici

|

1962-1963

|

tom 12

|

nr 2

191-197

4

On the epidermic effect for ordinary differential inequalities of the first order

47%

Mlak W.

Annales Polonici Mathematici

|

1956-1957

|

tom 3

|

nr 1

37-40

5

Limitations and dependence on parameter of solutions of non-stationary differential operator equations

47%

Mlak W.

Annales Polonici Mathematici

|

1959

|

tom 6

|

nr 3

305-322

6

On the Chaplighin method for partial differential equations of the first order

42%

Mlak W., Schechter E.

Annales Polonici Mathematici

|

1969-1970

|

tom 22

|

nr 1

1-18

7

The first boundary value problem for a non-linear parabolic equation

42%

Mlak W.

Annales Polonici Mathematici

|

1958-1959

|

tom 5

|

nr 3

257-262

8

The epidermic effect for differential inequalities of the first order

42%

Mlak W.

Annales Polonici Mathematici

|

1956-1957

|

tom 3

|

nr 1

157-164

9

Differential inequalities with unbounded operators in Banach spaces

42%

Mlak W.

Annales Polonici Mathematici

|

1960-1961

|

tom 9

|

nr 1

101-111

10

Integration of the first order partial differential inequality with distributions

42%

Mlak W.

Colloquium Mathematicum

|

1963

|

tom 10

|

nr 1

147-150

11

A note on approximation of solutions of abstract differential equations

42%

Mlak W.

Annales Polonici Mathematici

|

1961

|

tom 10

|

nr 3

273-278

12

Note on abstract differential inequalities and Chaplighin method

42%

Mlak W.

Annales Polonici Mathematici

|

1961

|

tom 10

|

nr 3

253-271

13

Integration of infinite systems of differential inequalities

36%

Mlak W., Olech C.

Annales Polonici Mathematici

|

1963

|

tom 13

|

nr 1

105-112

14

Remarks on the stability problem for parabolic equations

36%

Mlak W.

Annales Polonici Mathematici

|

1956-1957

|

tom 3

|

nr 2

343-348

15

Operators induced by transformations of Gaussian variables

36%

Mlak W.

Annales Polonici Mathematici

|

1985

|

tom 46

|

nr 1

197-212

16

Conditionally positive definite functions on linear spaces

36%

Mlak W.

Annales Polonici Mathematici

|

1983

|

tom 42

|

nr 1

187-239

17

Parabolic differential inequalities and Chaplighin's method

36%

Mlak W.

Annales Polonici Mathematici

|

1960

|

tom 8

|

nr 2

139-153

18

Dilations of Banach space operator valued functions

30%

Mlak W., Weron A.

Annales Polonici Mathematici

|

1980

|

tom 38

|

nr 3

295-303

19

Unitary dilations in case of ordered groups

30%

Mlak W.

Annales Polonici Mathematici

|

1965

|

tom 17

|

nr 3

321-328

20

Limitation of solutions of parabolic equations

30%

Mlak W.

Annales Polonici Mathematici

|

1958-1959

|

tom 5

|

nr 3

237-245

Ograniczanie wyników

Unitary dilations of contraction operators

An example of the equation $u_t = u_{xx} + f(x, t, u)$ with distinct maximum and minimum solutions of a mixed problem

Estimates of solutions of hyperbolic systems of differential equations in two independent variables

On the epidermic effect for ordinary differential inequalities of the first order

Limitations and dependence on parameter of solutions of non-stationary differential operator equations

On the Chaplighin method for partial differential equations of the first order

The first boundary value problem for a non-linear parabolic equation

The epidermic effect for differential inequalities of the first order

Differential inequalities with unbounded operators in Banach spaces

Integration of the first order partial differential inequality with distributions

A note on approximation of solutions of abstract differential equations

Note on abstract differential inequalities and Chaplighin method

Integration of infinite systems of differential inequalities

Remarks on the stability problem for parabolic equations

Operators induced by transformations of Gaussian variables

Conditionally positive definite functions on linear spaces

Parabolic differential inequalities and Chaplighin's method

Dilations of Banach space operator valued functions

Unitary dilations in case of ordered groups

Limitation of solutions of parabolic equations