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Sur la convergence des approximations successives pour l'équation $\frac{∂²z}{∂x∂y} = f(x,y,z,\frac{∂z}{∂x},\frac{∂z}{∂y})$

100%

Kisyński J.

Annales Polonici Mathematici

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1959-1960

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tom 7

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nr 2

233-240

2

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Comparison of solutions and successive approximations in the theory of the equation $∂^2z/∂x∂y = f(x, y, z, ∂z/∂x, ∂z/∂y)$

92%

Kisyński J., Pelczar A.

Instytut Matematyczny Polskiej Akademii Nauk

EN

CONTENTS Introduction........................................................................................................................................................................................................... 5 I. THE CAUCHY-DARBOUX PROBLEM IN FUNCTION CLASSES $C^1'*(Δ_{a,b};E)$ AND $L^{1,*}_1(Δ_{a,b};E)$......................... 7 1. Basic function classes ................................................................................................................................................................................... 7 2. The Cauchy-Darboux problem ...................................................................................................................................................................... 12 II. Comparison of solutions ............................................................................................................................................................................... 18 3. The growth estimations.................................................................................................................................................................................. 18 4. Maximal solutions............................................................................................................................................................................................ 26 5. A theorem on extension of inequalities........................................................................................................................................................ 28 6. Effective estimation in the case $M_1$, (b)................................................................................................................................................. 30 III. COMPARATIVE CRITERIA OF EXISTENCE AND UNIQUENESS OP SOLUTIONS OF THE CAUCHY-DARBOUX PROBLEM...................................................................................................................................................................................... 35 7. Basic classes of comparative functions...................................................................................................................................................... 35 8. Existence and uniqueness of solutions of the Cauchy-Darboux problem............................................................................................ 42 9. Remarks on the continuous dependence of solutions on boundary data and on the second member........................................ 47 10. Examples......................................................................................................................................................................................................... 49 BIBLIOGRAPHICAL REMARKS.......................................................................................................................................................................... 66 BIBLIOGRAPHY..................................................................................................................................................................................................... 68 INDEX OF SYMBOLS............................................................................................................................................................................................ 74

3

On M. Kac's probabilistic formula for the solution of the telegraphist's equation

67%

Kisyński J.

Annales Polonici Mathematici

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1974-1975

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tom 29

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nr 3

259-272

4

On second order hyperbolic equation with two independent variables

59%

Kisyński J.

Colloquium Mathematicum

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1970-1971

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tom 22

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nr 1

135-151

5

On operator-valued solutions of d'Alembert's functional equation, I

59%

Kisyński J.

Colloquium Mathematicum

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1971

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tom 23

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nr 1

107-114

6

Sur les équations hyperboliques avec petit paramètre

50%

Kisyński J.

Colloquium Mathematicum

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1963

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tom 10

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nr 2

331-343

7

A proof of the Trotter-Kato theorem on approximation of semi-groups

50%

Kisyński J.

Colloquium Mathematicum

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1967

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tom 18

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nr 1

181-184

8

On cosine operator functions and one-parameter groups of operators

50%

Kisyński J.

Studia Mathematica

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1972

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tom 44

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nr 1

93-105

9

Sur les opérateurs de Green des problèmes de Cauchy abstraits

50%

Kisyński J.

Studia Mathematica

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1963-1964

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tom 23

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nr 3

285-328

10

On operator valued solutions of d'Alembert's functional equation, II

50%

Kisyński J.

Studia Mathematica

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1972

|

tom 42

|

nr 1

43-66

11

A remark on continuity of one-parameter semi-groups of operators

50%

Kisyński J.

Colloquium Mathematicum

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1968

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tom 19

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nr 2

277-284

12

Remark on strongly additive set functions

42%

Kisyński J.

Fundamenta Mathematicae

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1968

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tom 63

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nr 3

327-332

13

On uniform symmetrization of analytic matrix functions

42%

Kisyński J.

Studia Mathematica

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1972

|

tom 42

|

nr 1

67-85

14

Sur les familles compactes de fonctions mesurables

42%

Kisyński J.

Colloquium Mathematicum

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1959-1960

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tom 7

|

nr 2

221-235

15

On the generation of tight measures

34%

Kisyński J.

Studia Mathematica

|

1968

|

tom 30

|

nr 2

141-151

16

Convergence du type L

34%

Kisyński J.

Colloquium Mathematicum

|

1959-1960

|

tom 7

|

nr 2

205-211

Ograniczanie wyników

7 Colloquium Mathematicum

5 Studia Mathematica

2 Annales Polonici Mathematici

1 Fundamenta Mathematicae

16 Kisyński J.

1 Pelczar A.

1 1974

3 1972

1 1971

2 1970

3 1968

1 1967

1 1964

1 1963

3 1960

Sur la convergence des approximations successives pour l'équation $\frac{∂²z}{∂x∂y} = f(x,y,z,\frac{∂z}{∂x},\frac{∂z}{∂y})$

Comparison of solutions and successive approximations in the theory of the equation $∂^2z/∂x∂y = f(x, y, z, ∂z/∂x, ∂z/∂y)$

On M. Kac's probabilistic formula for the solution of the telegraphist's equation

On second order hyperbolic equation with two independent variables

On operator-valued solutions of d'Alembert's functional equation, I

Sur les équations hyperboliques avec petit paramètre

A proof of the Trotter-Kato theorem on approximation of semi-groups

On cosine operator functions and one-parameter groups of operators

Sur les opérateurs de Green des problèmes de Cauchy abstraits

On operator valued solutions of d'Alembert's functional equation, II

A remark on continuity of one-parameter semi-groups of operators

Remark on strongly additive set functions

On uniform symmetrization of analytic matrix functions

Sur les familles compactes de fonctions mesurables

On the generation of tight measures

Convergence du type L