1. Introduction. The notion of uniqueness goes back to Cantor: a subset E of the unit circle Γ is said to be a set of uniqueness if the zero sequence is the only sequence (c

Pełen tekst

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INSTITUTE OF MATHEMATICS POLISH ACADEMY OF SCIENCES

WARSZAWA 1994

n

n∈Z

|n|≤m

n

int

m→∞

it

|n|→∞

(2)

0

n∈Z

n→−∞

0

0

+

0

n→−∞

0

0

+

ω0

0

ω0

0

n→∞

+

0

n→∞

+

0

+

n→∞

n→∞

1/p

1/p

n→−∞

1/p

n→∞

ω0

ω

ω

n<0

n≥0

(3)

+

+

n≥1

−n

n≥0

−n

+

+

1/p

n≥1

n−1

n≤0

n−1

0

z0

0

z0

0

1

P M

n∈Z

k

1

(4)

n

n∈Z

m→∞

|n|≤m

n

int

it

n

n

n=0

n

n

−1

n=−∞

n

n

m→∞

|n|≤m

n

int

it

1

n∈Z

1

z

E

1

n∈Z

r→1

Γ

p

p

−n

(5)

−1

−1

µ

0

it

µ

µ

µ

1

µ

µ

(6)

ζ

n≥1

n

n−1

n

0

n−1

n

n−1

n−1

0

ζ

ζ

ζ

ζ

+

1

n=0

(n)

+

+

+

+

+

+

+

+

+

+

+

+

+

−1

+

+

+

+

P M

n→∞

P M

n∈Z

+

+

+

+

+

+

+

0

+

+

+

+

+

(7)

P M

n→−∞

+

+

+

+

+

+

+

+

−n

−n

n

+

n

+

n

n

n

n

n

+

n

n≥1

+

+

n

n≥1

+

n→∞

n

1

n→∞

n

n→∞

n

n,p

p−1

m=0

n

m

n,p

m=p

n

m−p

n→∞

n,p

1

n,p

n→∞

n,p−1

n

n

n,p

n,p−1

+

−p

n→∞

n,p

n,p−1

1

n∈Z

+

n

+

+

n∈Z

+

n

n∈Z

n

+

n

n→∞

n

+

+

n+p

−n

p

−n

1

−p

n=0

n≥0

P M

n→∞

+

+

(8)

n

n≥1

pn

+

1/p

ζ

ζ

(p)

+

n

n→∞

pn

n

n→∞

pn

+

+

+

+

+

0

n→−∞

0

0

0

n≥0

0

0

(9)

µ

0

it

it

0

µ

µ

µ

n≤0

µ

2

µ

0

t0

0

it0

µ

0

0

−λ

0

ε

0

0

n→∞

+

ε

µ

0

n→∞

+

0

+

n→∞

(10)

0

+

|z|→1

Γ (0,r)

K

L

K

L

K

L

0

0

0

K

Γ (z0,ε(z))

0

K

L

n≥0

n→∞

τ

n∈Z

τ

τ

n∈Z

n∈Z

2

τ

n∈Z

(11)

τ

τ

n∈Z

τ

τ

τ

τ

τ

0

τ

0

τ

0

τ

K

L

n→−∞

+

n→∞

0

0

0

Γ (1,ε(z))

z−1

{1}

Γ (1,ε(z))

z−1

z−1

n→∞

+

n→−∞

n→∞

t→∞

ε

−ε

√−iz

n∈Z

ε

ε

ε

(12)

|z|→∞

Im z≥0

+

|z|→∞

+

x→∞

{1}

+

1/p

n→−∞

0

it

1/p

1/p

n

−q

pn

n

n

1/p

1/p

n(k)

1/p

n

n

m=0

n

m=1

n

1

m≥1

n

n≥1

kn

n

(13)

1/p

0

1/p

n→∞

+

α

1/p

0

1/p

n→∞

+

β

+

+

+

p∈Z

P M

1

P M

P M

ω

n≤0

n>0

ω

ω

n≤0

n>0

ω

n→∞

1/n

ω

0

ω

n→∞

n→∞

n

ω

(14)

n→∞

ω

p

n

n

+

n→∞

−1

n

n

1

n→∞

n

n

1

n→∞

n

n

−1

n

m<0

P M

p

p

p

p

p

m<0

pm

m>0

pm

ω

P M

p

ω

n<0

P M

1

n≥p

n

ω

p→∞

p

ω

0

n→−∞

n→∞

0

n≥1

1

ω

n

n≥1

n

1

ω

ω

1

n+1

1

n

ω

ω

−n−2

n

pn

(15)

ω

n→∞

1

n

ω

n

1

n

n≥1

n

0

n

0

n→∞

1

n

n≥1

n

0

ω

n→−∞

0

n→−∞

ζ

n→∞

ω

ω

n→∞

n→∞

n→∞

ω

ω0

0

ω

n→∞

n→∞

n≥1

−n

n≥1

−n

+

ω0

n≥1

−n

+

(16)

ω0

+

−int

A+(E)

ω0

+

1/p

+

n→∞

−n

1/p

−n

α

n≥1

−n

p

p

+

1/p

n→∞

ω

ω

ω

n→∞

ω−n

ω

n≥1

ω−n

π

−π

+

it

ζ

−n

k

−1

n∈Z

n

−n

n∈Z

(n)

Sp T

(17)

Sp T

Sp T

−1

−1

−1

−1

+

+

1

+

+

A

+

I

A

I

p

α

1/p

ζ

ζ

0

0+

+

0+

(18)

0+

0+

A

+

I

A

I

+

0

+

+

+

0+

+

+

+

n

(19)

+

1

+

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